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.
Homework Statement
A 5g bullet is fired horizontally into a 0.50kg block of wood resting on a frictionless table. The block, which is attached to a horizontal spring, retains the bullet and moves forward, compressing the spring. The block-bullet system goes into SHM with a frequency of 9Hz...
Homework Statement
On a horizontal, frictionless table, an open-topped 5.50kg box is attached to an ideal horizontal spring having force constant 365 N/m . Inside the box is a 3.44-kg stone. The system is oscillating with an amplitude of 7.50 . When the box has reached its maximum speed, the...
Homework Statement
On a frictionless, horizontal air track, a glider oscillates at the end of an ideal spring of force constant 2.20 N/cm . The graph in the figure shows the acceleration of the glider as a function of time.
Find the mass of the glider.
Homework Equations
T=...
A 2kg body, moving under the influence of a force constant of 3.16N/m, vibrates in SHM with an amplitude of 30mm. Determine the speed and the acceleration,
a) at the midpoint of the vibration (ie. zero displacement)
b) at the end of the path (ie. Max displacement)
c) at a point 20mm from the...
Homework Statement
A block with mass m =7 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.23 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.7 m/s. The block oscillates on the spring without...
Homework Statement
x = 0.20m*sin(0.44 rad/s * t)
Write the equation for the velocity of this object. Find the velocity at t = 4:0 s.
Homework Equations
The Attempt at a Solution
well, i know that v(t)= - wAsin(wt +\phi)
and we know the w = 0.44 rad/s
A = 0.20 s
t=4...
Homework Statement
A particle executes simple harmonic motion along a straight line with mean position at x=0, period 20s and amplitude 5cm. The (shortest) time in seconds taken by the particle to got from x=4cm to x=-3cm is?
The Attempt at a Solution
Let the equation be x=Asin(wt+Φ)...
Homework Statement
A man floating in water was spotted by fishermen on a boat. Before taking him on board, the man was put on a fish scale to see how much he weighed. The reading on the scale oscillated between 72kg and 178kg. The wave speed was measured to be 16 m/s. The wave height was 3 m...
Homework Statement
A block of mass 300 gm is attached to a spring with spring constant 1000 N/m. A smaller block of mass 100 gm is pushed against the first block, compressing the spring 5 cm. The coefficient of static friction between the two blocks is u = 0.2. The blocks are then released...
Homework Statement
1. Modeling. Functions.
A student measures the length L = 3 feet of a light (0.1 grams) string and the mass m = 7
kilograms of a small (radius of 0.0005 inches) bob at the end of the string.
The students also knows the value of acceleration due to gravity g = 9.8...
(This isn't homework)
I've been crating some notes, and noticed that we haven't been told one equation.
I know for:
\frac{d^2 x}{dt^2} = \frac{-kx}{m} -\frac{b}{m} \frac{dx}{dt}
I know the displacement is:
x = A \omega e^{-bt/2m} cos(\omega t+ \phi)
[Ie damping]
I know for...
Homework Statement
A 590.0 g mass oscillates with an amplitude of 11.4 cm on a spring whose spring constant is 27.7 N/m. At t=0.00 s the mass is 3.14 cm to the right of the equilibrium position and moving to the right.
Homework Equations
x(t)=Acos(Wt + phi)
The Attempt at a Solution...
Homework Statement
In the given figure, all the springs and pulley are ideal and surface is frictionless. The rod is massless. The time period of horizontal oscillations of the block is?
The Attempt at a Solution
I used two different approaches and both give different and wrong...
Homework Statement
A body is undergoing S.H.M. of amplitude 4 x 10-2 m and with a maximum
speedo f 0.20m s-1. Calculate the period of the oscillation given that the velocity,
v, of a body undergoing S.H.M. is ""v= omega sq.rt of A^2 - x ^2"" , where trl is the angular
velocity, A is the...
A block having mass m and charge +Q is connected to a spring having constant k. The block lies on a frictionless horizontal track, and the system is immersed in a uniform electric field of magnitude E, directed as shown in the figure below. The block is released from rest when the spring is...
Homework Statement
A 2-kg block is dropped from a height of 0.45 m above an uncompressed spring. The spring has an elastic constant of 200 N/m and negligible mass. The block strikes the end of the spring and sticks to it.
(a) Determine the speed of the block at impact
(b) Determine the period...
Homework Statement
Two pendulums of time periods 3s and 7 s respectively start oscillating simultaneously from two opposite extreme positions. After how much time they will be in the same phase?
Homework Equations
The Attempt at a Solution
Now what exactly is the question...
Homework Statement
A cylinder of radius R and mass m is suspended using stainless steel
wires attached to fixed supports, so that it can rotate about its axis.
When the cylinder is rotated by an angle a the wires exert a torque
which tends to bring it back to the equilibrium position at a...
Simple harmonic motion! :(
Homework Statement
A 65-kg person jumps from a window to a fire net 18m below, which stretches the net 1.1m. Assume that the net behaves like a simple spring, and (a) calculate how much it would stretch if the same person were lying in it. (b) How much would it...
[b]1. A 14.7g mass is attached to a frictionless horizontal spring. After the spring was stretched a certain distance and released, its maximum speed was found to be 4.22 m/s. If the speed at x = -2.84 cm is 1.63 m/s, what is the frequency of the oscillating spring?
[b]2. PEe = kx^2/2 E=KE...
1.
A mass of 0.5 kg hangs on a spring. The stiffness of the spring is 100 N/m, and the mechanical resistance is 1.4 kg/s. The force (N) driving the system is f=2cost5t.
(a) What will be the steady-state values of the displacement amplitude, speed amplitude, and average power dissipation...
1. An oscillator with mass 0.5 kg, stiffness 100 N/m, and mechanical resistance 1.4 kg/s is driven by a sinusoidal force of amplitude 2 N. Plot the speed amplitude and the phase angle between the force and speed as a function of the driving frequency and find the frequencies for which the phase...
Homework Statement
When a mass is hung from a spring, the spring elongates by 10.6cm. What will the period of the resulting oscillations be if the mass is displaced from equilibrium?
Homework Equations
T=2(pi)\sqrt{m/k}
The Attempt at a Solution
I have no clue what do with this...
Homework Statement
An electric dipole in a uniform horizontal electric field is displaced slightly from its equilibrium position, where theta is small. The separation of the charges is 2a, and each of the two particles has mass m. Assuming the dipole is released from this position, show that...
Homework Statement
I need help finding velocity as a function of position, the t in the argument of tan, causes a problem for me when integrating. can someone help, maybe my approach is completely off, i am trying to fing the unknown phi, knowing the velocity and acceletation when position...
Homework Statement
A simple pendulum is 5.20 m long. What is the period of simple harmonic motion for this pendulum if it is hanging in an elevator that is accelerating upward at 5.90 m/s2?
Homework Equations
T=2pi*(sqrt(L/g))
The Attempt at a Solution
all I did was plug in the...
Homework Statement
A mass is oscillating on a spring with a period of 1.45 s. At t = 0 the mass has zero speed and is at x = 8.80 cm. What is the magnitude of the acceleration at t = 2.30 s?
Homework Equations
x(t)=Acos(wt + phi)
a(t)=-Aw^2cos(wt + phi)
a=w^2x
T=2pi/w
The Attempt...
Homework Statement
I have that a oscillating mass undergoes shm. It is accelerated (forced oscillation) by 1ms^-2, for time pi/2 as it goes through the origin and then accelerated by -1ms^-2 for another time pi/2, then it is at the origin after the second acceleration.
I need to determine...
Could anybody temme what wuld happen to the time period and the amplitude of oscillations if a mass attaching to a ruler, lying horizontally on the table, is broken ...then what effect would this have on the amplitude and time period of oscillations?
I say that amplitude would increase...
Simple Harmonic Motion Question... Advise required please!
A vehicle engine has a stroke of 180mm. The motion of the piston is simple harmonic.
calculate max linear velocity and acceleration at 4200rpm?
Calculate max force to the crankshaft if the piston has an effictive mass of .35kg at an...
Homework Statement
The rise and fall of water in a harbour is simple harmonic. The depth of water varies between 5.0 m at low tide and 9.0 m at high tide. The time between sucessive low tides is 12 hours. A ship, which requires a minimum depth of 6.0 m approaches the harbour at low tide, how...
Homework Statement
A spring with spring constant 17.0 N/m hangs from the ceiling. A 530 g ball is attached to the spring and allowed to come to rest. It is then pulled down 7.00 cm and released.
What is the time constant if the ball's amplitude has decreased to 3.50 cm after 41.0...
Homework Statement
The position of a an air-track cart that is oscillating on a spring is given by (12.5cm)cos[(18.0s-1)t].
At what value t after t=0 is the cart first located at x=12.2 cm?
The Attempt at a Solution
12.2 cm = (12.5cm)cos[(18.0s^-1)t].
How do I factor t out?
Thanks
Homework Statement
A 100-g block hangs from a spring with k = 5.2 N/m. At t = 0 s, the block is .20 m below the equilibrium position and moving upward with a speed of 2.10 m/s. What is the block's speed when the displacement from equilibrium is .324 m?
Homework Equations
w0=sqrt(k/m)...
Homework Statement
A particle oscillates with an s.h.m of amplitude 50mm and a maximum speed of 0.25 m/s. Calculate the pulsatance, period and maximum acceleration
Homework Equations
x = a sin(wt)
dx/dt=awcos(wt)
d2x/dt2=aw^2sin(wt)
Put in x=0.05sin(wt)
0.25=0.05wcos(wt)...
Homework Statement
A 450 g object oscillates from a vertically hanging light spring once every .55 s. The object is released with the spring compressed by 10 cm from the equilibrium position. What is the velocity of the object 3.00 s after it is released?
Homework Equations...
Homework Statement
A vertical spring, fixed at the upper end, has a mass attached to the lower end. When the
spring is given a small extension it was observed to oscillate at a rate of 45 cycles per
minute. When an additional 160g mass is attached to the spring, it oscillated at a rate of...
simple harmonic motion !
Homework Statement
An ideal spring has a spring constant k=25N/M and is suspended vertically. A 1kg object is attatched to the unstrechted spring and released. It then performs ocillations.
What is the magnitude of the acceleration of the body when the extension of...
Simple Harmonic Motion Questions-springs
Homework Statement
A .20 kg mass is sliding on a horizontal frictionless air track with a speed of 3 m/s when it instantaneously hits and sticks to a 1.3 kg mass initially at rest on the track. The 1.3 kg mass is connected to one end of a massless...
Homework Statement
A ball dropped from a height of 4m makes a perfectly elastic collision with the ground. Assuming that no energy is lost due to air resistance.
show the motion is periodic
determine the period of the motion
Homework Equations
yf-yi=vit+1/2ayt2
a=-(w2)x
a=9.8m/s2...
Homework Statement
Im confused about what exactly is the period and amplitude of a spring... Is the period -during ocillation-from top to bottom back to top? or vice versa. and is the amplitude 1/4 of the period?
Homework Equations
The Attempt at a Solution
Homework Statement
An ideal spring has a spring constant k=25N/M and is suspended vertically. A 1kg object is attatched to the unstrechted spring and released. It then performs ocillations.
What is the magnitude of the acceleration of the body when the extension of the spring is at maximum...
Homework Statement
I have been stuck on this question for quite some time. I'm trying to study for the test and actually have the answer, but I can't figure it out. The answer is 1.3X10-6cm/s2
The following graph represents an object oscillating in simple harmonic motion. What is the...
Homework Statement
For a particle in simple harmonic motion, show that vmax = (pi/2) vaverage, where vaverage is the average speed during one cycle of the motion.
Homework Equations
v(t) = -vmaxsin(wt + phi)
vmax = 2piA/ T = wA
The Attempt at a Solution
I'm really not sure at...
Homework Statement
a 700 g cylinder of base area a=30 cm^2 and height 40 cm is floating upright in water. A 50 g mass, resting on top of the cylinder is suddenly removed. find the restoring force.
Homework Equations
The Attempt at a Solution
Homework Statement
A piston in an automobile engine is in simple
harmonic motion. Its amplitude of oscillation
from the equilibrium (centered) position is
±6.87 cm and its mass is 1.472 kg.
Find the maximum velocity of the piston
when the auto engine is running at the rate of
3220...
Homework Statement
I am wanting to learn how to rearrange equations for simple harmonic motion equations (I am new to LaTeX so gimme a break!) mostly to find time (t) as the subject, but I am not very good at rearranging equations with sin/cos etc and want to get better at it, partly homework...
Homework Statement
In static equilibrium a spring is stretched 0.25 m by a hanging mass. If the system is initially moved up to the unstretched position and released with zero velocity, determine position of the mass (in m) after 4.2s. Take the equilibrium position to be zero and up the...
Phase Angle / Phase Question - Simple Harmonic Motion
Homework Statement
If I were given a function of displacement for simple harmonic motion in the form of:
x = Acos(\omegat + \phi)
Would the phase angle, \phi, always be the same? Say if I derived the equations into forms for...