What is Harmonic motion: Definition and 1000 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.
A damped harmonic motion starts from rest at time t=0 with displacement A0 has the equation:
x(t) = A0/cos (delta)*e^(-t/tau) *cos (w't + delta)
w' is the angular frequency, tau is the time constant and delta is given by:
tan (delta) = - (1/w' tau)
find the time when the maximum...
Homework Statement
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
At t = 0 a block with mass M = 5 kg moves with a velocity v = 2 m/s at position xo = -.33 m from the equilibrium position of the spring. The block is attached to a massless spring of spring constant k = 61.2 N/m and slides on a frictionless surface. At what time will the...
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...
harmonic motion with friction x(t)=...
Homework Statement
Anybody knows what´s the equation x(t)=... for harmonic motion with friction ?
Homework Equations
For exemple, a string-block sistem with friction ?
I need determine the position of block at t instant.
The Attempt at a Solution
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...
Homework Statement
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...
Homework Statement
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...
Is the oscillation period T ( T = 2╥ * sqrt(M/k) ) independent of the Amplitude of the motion? I mean the equation shows that it is but I'm not totally convinced.
For example, if a massless spring of k = 6 and M = 0.04 has the mass pulled down (i) 0.04m and then (ii) 0.10m. Will the...
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?
Homework Statement
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.
Homework Statement
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...
Homework Statement
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...
Homework Statement
A particle of mass 'm' is subject to a spring force, '-kx', and also a driving force, Fd*cos(wdt). But there is no damping force. Find the particular solution for x(t) by guessing x(t) = A*cos(wdt) + B*sin(wdt). If you write this in the form C*cos(wdt - \phi), where C >...
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...
1. Homework Statement
-A pendulum with a length of 1.00 m is released from an initial angle of 15.0 degrees.
After 1,000 seconds, its amplitude is reduced to friction by 5.50 degrees. What is the value of b/2m?
Homework Equations
In simple harmonic motion, a simple...
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...
Homework Statement
The position of a particle is given by x = 4.6 cos (pi)t, where x is in meters and t is in seconds.
(a) Find the maximum speed and maximum acceleration of the particle.
I've already solved these by finding the first and second derivatives of the above x.
v =...
Homework Statement
A small bock that has a mass equal to M rest on a piston that is vibrating vertically with simply harmonic motion described by the formula y = Asin(wt)
a) Show that the block will leave the piston if w2A > g.
b) If w2A = 3g and A = 15 cm, at what time will the block...
A body with SHM has a velocity of 1.3 m/s at a distance of 1.0m from the mean position, and a velocity of 1.0 m/s at a distance of 1.3m from the mean position. Find:
a) The amplitude of the motion.
b) The velocity of the mid-position.
c) The time elapsed between the instants when the body...
Homework Statement
Two 100g blocks are held 80 cm above a table. As shown in the figure, one of them is just touching a 80cm-long spring. The two blocks are released at the same time. The block on the left just hits the table at exactly the same instant as the block on the right first...
Homework Statement
Automobile of mass m=2000kg has a suspension that sags 10 cm when the entire auto is placed on it. The amp. of oscillation decreases 50% with every complete oscillation. Solve for (a) spring constant k and (b)the damping constant b for one wheel (assuming each wheel...
A block rides on a piston that is moving vertically with simple harmonic motion. (a) If the SHM has period 1.0 s, at what amplitude of motion will the block and piston separate? (b) If the piston has an amplitude of 5.0 cm, what is the maximum frequency for which the block and piston will be in...
I am completely and totally lost...
Homework Statement
The motion of an object is simple harmonic with equation of motion x = (27.1 m) sin(16.0 t /s + 0.7). At what time after t = 0 will the displacement reach its first maximum (where velocity equals zero)?
Homework Equations
x = Asin(wt)
Simple Harmonic Motion .. an Object Attached to a Spring!
Hi everybody :smile: .. I'm glad that i joined this forum so that i can help people and benefit at the same time :) .. i wanted to start with this problem right here ,, and hope that i get the hand from you :)
it's a question I've...
Reviewing for the MCAT this Christmas, most of physics is going okay except I run into a few areas I was never familiar with to be begin with.
Homework Statement
By what percentage does the frequency diminish in a horizontal spring mass system where k=1x10^3 N/m and m= 4 kg if the motion is...
Homework Statement
A mass-spring system oscillates with an amplitude of 0.024m. The spring constant is 250 N/m and the mass is 0.494kg.
Calculate the maximum acceleration of the mass-spring system.
Homework Equations
F=-kx
Ue=1/2kx^2
F=ma
The Attempt at a Solution
So, I...
Homework Statement
The motion of an object is simple harmonic with equation of motion x = (27.1 m) sin(16.0 t /s + 0.7). At what time after t = 0 will the displacement reach its first maximum (where velocity equals zero)?
Homework Equations
(displacement)=Asin(freq.*t+phase)
The...
Homework Statement
Prove that there exists a number A>0 and \phi such that acos(ct)+bsin(ct)=Acos(ct-\phi).
Homework Equations
a,b,c are predermined constants where c>0. From this equation I can justify conclusions regarding the amplitude, frequency, and so forth of a simple harmonic...
A 2.1 g spider is dangling at the end of a silk thread. You can make the spider bounce up and down on the thread by tapping lightly on his feet with a pencil. You soon discover that you can give the spider the largest amplitude on his little bungee cord if you tap at a frequency of 0.8 Hz. What...