What is Simple harmonic motion: Definition and 913 Discussions
In mechanics and physics, simple harmonic motion (sometimes abbreviated SHM) is a special type of periodic motion where the restoring force on the moving object is directly proportional to the object's displacement magnitude and acts towards the object's equilibrium position. It results in an oscillation which, if uninhibited by friction or any other dissipation of energy, continues indefinitely.
Simple harmonic motion can serve as a mathematical model for a variety of motions, but is typified by the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law. The motion is sinusoidal in time and demonstrates a single resonant frequency. Other phenomena can be modeled by simple harmonic motion, including the motion of a simple pendulum, although for it to be an accurate model, the net force on the object at the end of the pendulum must be proportional to the displacement (and even so, it is only a good approximation when the angle of the swing is small; see small-angle approximation). Simple harmonic motion can also be used to model molecular vibration as well.
Simple harmonic motion provides a basis for the characterization of more complicated periodic motion through the techniques of Fourier analysis.
Homework Statement
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As shown in the figure, one end (O) of a uniform rod of length L and mass M is pivoted to a wall. Two horizontal springs with force constants k1 and k2 are attached to the other end (P) of the rod. When the rod is...
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A negatively charged particle -q is placed at the center of a uniformly charged ring of radius a having positive charge Q. The particle, confined to move along the x-axis, is moved a small distance x along the axis (x << a) and released. Show that th eparticle oscillates in...
Hello everyone, I'm new here.
I'll just post my question- hopefully someone can answer.
A 2.00 kg block situated on a rough incline is connected to a spring of negligible mass having a spring constant of 100 n/m. The pulley is frictionless. The block is released from rest when the spring is...
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A block is attached to a horizontal spring. On top of this block rests another block. The two-block system slides back and forth in simple harmonic motion on a frictionless horizontal surface. At one extreme end of the oscillation cycle, where the blocks come to a momentary...
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A particle executes simple harmonic motion with an amplitude of 2.51cm. At what positive displacement from the midpoint of its motion does its speed equal one half of its max speed?
Homework Equations
A=2.51 cm
x(t) = Acos(wt)
v(t) = -Awsin(wt)
vmax = |-Aw|
The...
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A block of unknown mass is attached to a spring of spring constant 6.7N/m and undergoes simple harmonic motion with an amplitude of 7.8 cm. When the mass is halfway between its equilibrium position and its max endpoint, its speed is measured to be 38.5 cm/s.
(a) Calculate...
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Two identical particles, each having a charge of +q are fixed in space and separated by a distance d. A third particle with charge -Q is free to move and lies initially at rest on the perpendicular bisector of the two fixed charges a distance x from the midpoint between the...
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A hanging spring stretches by 35.0cm when an object of mass 450g is hung on it at rest. In this situation we define its position as x=0. The object is pulled down an additional 18.0cm and released from rest to oscillate without friction. What is its position x at a moment...
The total movement of a body oscillating with simple harmonic motion is 200mm. If the frequency of oscillation is 6Hz, determine the maximum velocity and maximum acceleration of the body.
I missed the class when this was done so I haven't got the notes. I am not sure if this is right but I...
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A 50 g block is hung from a vertical spring. The spring constant is 4 N/m. We let go of the block when the spring is not stretched.What is the maximal stretch of the spring?
2. Equations
Fs=k times x
The Attempt at a Solution
At the maximal stretch, the block is at...
Homework Statement
Calculate the total energy of a 2kg mass that is undergoing simple harmonic motion with an amplitude of 1cm and and frequency of 16Hz.
Homework Equations
ma = -w^2x
The Attempt at a Solution
The first thing I thought was using the general solution of x(t) = A...
hi i am having trouble grasping this question
A block of mass M hangs from a rubber cord. The block is supported so that the cord is not stretched. The unstretched length of the cord is L0, and its mass is m, much less than M. The "spring constant" for the cord is k. The block is released and...
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A table moves up and down in SHM of period 1 second. Find the amplitude it can have at which objects on the table just comence to lose contact with the table.
The Attempt at a Solution
How do I need to solve this problem? I'm only given the period from which I can...
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A 0.20-kilogram mass is sliding on a horizontal, frictionless air track with a speed of 3.0 meters per second when it instantaneously hits and sticks to a 1.3-kilogram mass initially at rest on the track. The 1.3-kilogram mass is connected to one end of a massless spring...
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A mass on a spring obeys SHM.Given that the mass is initially at the equilibrium position,has an initial velocity of 2m/s,and a nastural frequency of 2 rad/s,Find A and φ
After 13.2 sec what's the displacement of the mass
Homework Equations
ψ=Αcos(ωt+φ)
The Attempt...
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A spring with stiffness s is suspended vertically with a mass m attached to it's free end. When the mass comes to rest the spring is found to have been stretched by 0.0981m. The mass is then pulled down a further 0.1m, released from rest and found to execute SHM.
We're...
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A 100 g ball attached to a spring with spring constant 2.9 oscillates horizontally on a frictionless table. Its velocity is 20 cm/s when x = 4.8 cm.
What is the ball's maximum acceleration?
which I found to be amax= 180 cm/s^2
What is the ball's position when the...
Homework Statement
Please find the question in the attachment,i've attached it because it includes a graph
Homework Equations
a=-(omega)^2.x
T=2.pie/omega
Vmax=omega.A
The Attempt at a Solution
for part b i used the first equation a=-(omega)^2.x to find omega and then substituted...
Homework Statement
For my problem, I have two springs that have the same length, but different masses and spring constants. Both springs are secured at one end to a holder and at the other ends are connected to a single mass.
My question is how do I find the angular velocity? Since the...
A hanging wire is 1.80 m long. When a 60.0 kg ball is suspended from the wire, the wire stretches 2.00 mm. If the ball is pulled down a small additional distance and released, at what frequency will it vibrate? Assume that the stress on the wire is less than the proportional limit.
I have...
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The balance wheel of an old fashioned watch oscillates with an angular amplitude π rad and period of 0.500 s. Find the maximum angular speed of the wheel.
Homework Equations
There are a lot of equations in this chapter and I don't even know where to start :confused...
F=-kx when talking about a mass at the end of a horizontal spring
therefore ma=-kx
rearranging we get a= -(k/m)x
then it says if we define ω2=k/m we then have a generic form :
a= -ω2x
My question is what does "if we define ω2=k/m" mean? where does this come from?is it just any random...
Homework Statement
I am having a hard time solving this problem and this is my last chance to solve it before it is due and I have to do this for a test tomorrow.
A simple harmonic oscillator consists of a block of mass 3.90 kg attached to a spring of spring constant 330 N/m. When t = 0.570...
Homework Statement
A 500g block on a spring is pulled 20cm and released. The motion has a period 0.8s.
What is the velocity when the block is 15.4cm from the equilibrium?
Homework Equations
Etotal = 0.5kx2 + 0.5mv2
w = \sqrt{k/m}
w = 2pi*f
f = 1/T
The Attempt at a Solution...
I have 4 quick questions about the position wave equation, x = Acos(omega*t + delta), can someone please explain this (in very simple language) thanks!
1. Why do we have to use cos? why not sin? wouldn't sine be better so that amplitude starts at zero also? using cos must make things easier...
Homework Statement
A platform moves up and down in SHM, with amplitude 0.035 m. Resting on top of the platform is a block of wood. What is the shortest period of motion for the platform so that the block will remain in constant contact with it?
Homework Equations...
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A small hole is drilled in a meter stick is to act as a pivot. The meter stick swings in a short arc as a physical pendulum. How far from the center of mass should the pivot point be for a period of 1.65 seconds?
Homework Equations
Moment of inertia as given in book...
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Another SHM question. Thanks for the help on my first one.
The block is at x0 = +5 cm with a positive velocity V0 at time t = 0. Its motion is SHM with amplitude 10 cm and period 2 seconds. If x(t) = Acos(wt + \varphi), the phase constant \varphi should be:
Homework...
Homework Statement
An object moves with simple harmonic motion. If the amplitude and the period are both doubled, the object's maximum speed is:
A) Quartered
B) Halved
C) Quadrupled
D) Doubled
E) UnchangedHomework Equations
x(t) = Acos(wt + \varphi)
v(t) = -wAsin(wt + \varphi)The Attempt at a...
Homework Statement
A 14.3 g bullet is fired into and embeds itself
in a 2.76 kg block attached to a spring with a
spring constant of 18.4 N/m and whose mass
is negligible.
How far is the spring compressed if the
bullet has a speed of 247 m/s just before it
strikes the block, and the block...
Homework Statement
A 2.10-kg block is suspended from a spring with a spring constant of 280.0 N/m. A 0.070-kg bullet is fired into the block from directly below with a speed of 220.0 m/s and is embedded in the block. Find the amplitude of the subsequent motion.
-What fraction of the...
Homework Statement
Part 1:
A block of mass 0.3 kg is attached to a
spring of spring constant 23 N/m on a fric-
tionless track. The block moves in simple har-
monic motion with amplitude 0.2 m. While
passing through the equilibrium point from
left to right, the block is struck by a bullet,
which...
A uniform rod of length , pivoted at one end, is set into small oscillation in a vertical plane. Show that the period of oscillation is T=2\pi\sqrt{\frac{3L}{2g}}
Shouldn't the period be
T = 2\pi\sqrt{\frac{L}{g}}
regardless of the mass and dimension of the object?
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What is the equation for the displacement of a sin wave (eg something in SHM)?
My book says x(t) = Acos(ωt + ɸ0)
My prof's notes say y(x,t) = Asin(ωt - kx + ɸ0)
Homework Equations
The Attempt at a Solution
I'm not confused about why one is sin and the...
The problem statement, with all known data/variables.
A 500 g object is moving a horizontal frictionless surface. Its displacement from the origin is given by the equation: x(t) = (3.50m)\sin{[(\frac{\pi}{2})t + \frac{5\pi}{4}]}.
a)what kind of motion is this?
b)what is the amplitude of...
Homework Statement
Here is a position-time graph for a ball on a spring in SHM.
What is the phase of the particle at point a on the graph?
Homework Equations
phase = ωt + ɸ0The Attempt at a Solution
First I found the initial phase, ɸ0. 0.5A / A = 0.5 = cos(ɸ0). Then ɸ0 = -π/3. It's negative...
Yeah I got this question and I'm just wondering if I'm doing it right.
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A spring normally 10cm long and whose force constant is 150 n/m is connected to another spring normally 20cm long and whose force constant is 100 n/m. The combination is then pulled out so that its...
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A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27cm and a frequency of 2.55Hz. How long does it take to travel 11.43cm?
Homework Equations
x=A*cos(w*t)
w=2\pi*f
w=2\pi/T
T=1/f
The Attempt at a Solution
I can't...
If we have 2 simple pendulums, (one longer than the other) oscillating in SHM in step. The next time they are in step is after 20 seconds has elapsed, during which the time the longer pendulum has completed exactly 10 oscillations. Find the string lengths
I found that the length of the long...
There are two masses both M +a and -a apart with respect to the origin on the y axis. A third mass, m, is x away from the origin. Due to gravity it will oscillate back and forth. What is T
Also, how can I use conservation of energy to find the velocity of the third mass m when it reaches the...
If we have two pendulums (one with periodic time 1.0 s and the other 0.5 s) and the two are set off oscillating in step, how can we find out the number of times they will be in step over a period of 60 s??
Help much appreciated! thanks!
Homework Statement
There's a block attached to a spring on a frictionless surface that oscillates back and forth. (Assume no damping).
At t=0, the potential energy in the spring is 25% of the maximum potential energy.
Kinetic energy decreases with time at t=0, and at t=2, the kinetic energy...
Homework Statement
A block attached to a spring with unknown spring constant oscillates with a period of 2.0 seconds. What is the period if a) the mass is doubled? b) the mass is halved? c) the amplitude is doubled? d) the spring constant is doubled?
Homework Equations
f=1/2pi(square...
Homework Statement
Consider the simple harmonic motion of a block attached to a spring on a horizontal surface (assume no damping to begin with). At t = 0, the potential energy in the spring is 25% of the maximum potential energy during this motion. Moreover, the kinetic energy of the block...
This topic has proved itself to be a hard one in, in terms of looking it up online. I'm interested in simple harmonic motion, in specific that of a tuning fork vibrating between two electromagnetic devices, a microphone ad a detector.
My main interest in it is to write a lab report about an...
An 85.0 kg person steps into a car of mass 2400 kg, causing it to sink 2.35 cm on its springs. If started into vertical oscillation, and assuming no damping, at what frequency will the car and passenger vibrate on these springs?
w= Sqrt (k/m), mg=kx, perhaps?
The way I treated the...
Homework Statement
A 0.50 kg particle executes linear harmonic motion about the point x = 0.0. At t= 1.0, it has a displacement x = 0.50m and a speed of 5.0 m/s to the right. The frequency of the motion is 2Hz. Determine (a) the spring constant, (b) the amplitude of the motion, (c) the...
In Simple harmonic motion: Acceleration = -W^2 x (W being omega, rads per sec. and x beind displacement (distance if you will) ) Omega is a constant
but why is acceleration proportional to the NEGATIVE displacement, in other words, why MINUS??
Help appreciated. Thanks in advance!
Homework Statement
A particle of mass m begins at rest from x = +24 cm and oscillates about its equilibrium position at x = 0 with a period of 1.4 s. Write expressions for the following. (Enter your numerical values to two decimal places.)
(a) the position x as a function of t
I solved...