# 18 Simple Harmonic Motion SHM

This is the final section of periodic motion which expands on circular motion to include more complex ideas. You must study circular motion first before you do this topic.

18 SHM Student booklet

18 SHM

V Shaped Pendulum Results

SHM Focus Education Results

Maths Skills angles

A3 slide to compare motion

SHM Data Damping

18.6 damping analysis sheet

18.6 Forced resonance results

## Forced Oscillation Resonance

See how a mass spring system has a frequency at which it oscillates freely.

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Forced Oscillation Resonance

See how a mass spring system has a frequency at which it oscillates freely.

See how a mass spring system has a frequency at which it oscillates freely.

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SHM and Circular motion with Phase change

Very cool SHM experiment. Watch to the end to find out the length of the [...]

Very cool SHM experiment. Watch to the end to find out the length of the pendulum. Use the time on the video to compare.

If you work out the cycle time from 1min to 1 min 14s. The ball spins around 10 times. This gives a period T = 1.4s

The string is 0.43cm long which gives a theoretical period time T = 1.32s

Interestingly if you work out the expected length to match the pendulum is should be 48.7cmShow More active

Lisajous Figures

Lissajous curves can be generated using an oscilloscope (as illustrated). [...]

Lissajous curves can be generated using an oscilloscope (as illustrated).

Two phase-shifted sinusoid inputs are applied to the oscilloscope in X-Y mode and the phase relationship between the signals is presented as a Lissajous figure.

In the professional audio world, this method is used for realtime analysis of the phase relationship between the left and right channels of a stereo audio signal.Show More active

Wave Phase

http://www.brightstorm.com/science/physics SUBSCRIBE FOR All OUR VIDEOS! [...]

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Oscillations Demo: Mass Spring System

This demonstration investigates the dependence of the period of the [...]

This demonstration investigates the dependence of the period of the mass-spring system on the mass, the spring constant, and the amplitude.

This demonstration was created at Utah State University by Professor Boyd F. Edwards, assisted by James Coburn (demonstration specialist), David Evans (videography), and Rebecca Whitney (closed captions), with support from Jan Sojka, Physics Department Head, and Robert Wagner, Executive Vice Provost and Dean of Academic and Instructional Services.Show More active

Tom Altman and SHM at the Exploriatorium

The High School Physics Project: Classic demonstrations of Simple Harmonic [...]

The High School Physics Project: Classic demonstrations of Simple Harmonic Motion.

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Simple Harmonic Motion Visualized

An old animation. Tools - Cinema 4D, Adobe Premiere Pro

An old animation.

Tools - Cinema 4D, Adobe Premiere Pro

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SHM OF TROLLEY

With s- and v-t graphs

With s- and v-t graphs

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Simple Harmonic Motion

A description of Simple Harmonic Motion, including its definition, and [...]

A description of Simple Harmonic Motion, including its definition, and examples of SHM in the form of oscillating springs and pendulums.

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Simple Harmonic Motion and Energy Conservation

Introduces energy conservation for simple harmonic motion problems. This is [...]

Introduces energy conservation for simple harmonic motion problems. This is at the AP Physics level.

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Kinetic and Potential Energy in SHM #6

Kinetic and potential energy in SHM is a function of position of the mass [...]

Kinetic and potential energy in SHM is a function of position of the mass relative to the equilibrium position. Are you "PHYSICS READY?" : https://the-science-cube.teachable.com/

Find how a Kinetic energy and a Potential energy graph can be plotted and important inferences made form the graph.

Who can use:

Class 11 and 12 students (CBSE, ICSE, NCERT)

IIT-JEE Preparation (JEE Main and JEE advanced)

K-12

Advanced Placement (AP Physics)

Subject SAT

Hello and welcome back to another lesson in SHM and what we are going to learn in this lesson is how the potential and kinetic energy of this system changes during time period T. And if you sum up the Potential and Kinetic Energy at various times, you can also establish how the total energy of the system will change. Well, as we move ahead, what you will find is that total energy of the system actually remains constant which should not be surprising to you since this system is also following the law of conservation of energy, that is if there is no friction in the system.

So the potential energy stored is a spring is given by the expression PE = ½ k x (sq.)

Well we can write this as PE = ½ k A(sq.) cos sq.) (wt + phi)

The Kinetic energy of such a system is given by the familiar equation KE = 1/2m v (sq.) that can be written as

SO we can write that the total mechanical energy =

Well if we add the two, the expression we get is E = U + KE = ½ kA (sq.)

Lets also go ahead and plot values of PE and KE in a graph.

So what we can say is that the springiness of the spring that is represented by k is what cause potential energy to get stored and the inertia of the mass is what provides the KE to the mass.

In other words the system has part energy stored in the spring which is the potential energy and the other part is in the block that is the KE

We can also use the equation

To find velocity of the mass at various points

The plus minus sign clearly indicating that the velocity is negative at extreme right that is moving towards left and positive at extreme left, when the block is moving towards the right.

And you can actually test this equation by putting various x values and you’ll get the correct answer.

So if we were to put x = A, the v value reduces to zero which is true. You get the same zero velocity of you put x = -A.

At x = 0, you’ll find the velocity becomes

Lets see these graphs a little closely. What you can see is that if at any instant the PE is this then the KE would be this. Infact if you are given a graph that has PE and the total Mech energy, you can establish the KE. All you need to do is measure the balance height which would be nothing but KE.

Let us now simulate one complete cycle of the mass and see how PE and KE changes with time.

Well you can see that as the mass starts moving, the KE is zero because the mass is at rest and PE is maximum because the spring is totally stretched and as the mass moves to the left, the KE increases and the PE goes down and at the middle the mass has maximum KE and zero PE. But as the mass starts moving away from the equilibrium position to the left, the mass again starst gaining PE and losing KE till the PE becomes max at the extreme left and KE becomes zero.

Ok, let us now see how displacement X, Velocity v, acceleration a, potential energy U and Kinetic energy K changes as the mass oscillates over several cycles. Again, do not try to see al graphs at one time. Take two graphs at a time. See how KE changes with velocity and how the potential energy changes with position X. You can pair any two graphs and see how the values change as the mass oscillatesShow More active

Barton's Pendulum

First demonstrated by Prof Edwin Henry Barton FRS FRSE (1858–1925), [...]

First demonstrated by Prof Edwin Henry Barton FRS FRSE (1858–1925), Professor of Physics at University College, Nottingham, who had a particular interest in the movement and behavior of spherical bodies, the Barton's pendulums experiment demonstrates the physical phenomenon of resonance and the response of pendulums to vibration at, below and above their resonant frequencies.

In its simplest construction, approximately 10 different pendulums are hung from one common string. This system vibrates at the resonance frequency of a driver pendulum, causing the target pendulum to swing with the maximum amplitude.

The other pendulums to the side do not move as well, thus demonstrating how torquing a pendulum at its resonance frequency is most efficient. The driver pendulum should lead by pi/2 to the driven.

The driver may be a very heavy pendulum also attached to this common string; the driver is set to swing and move the whole system.Show More active

Barton's Pendulum 2nd Version "The Snake"

First demonstrated by Prof Edwin Henry Barton FRS FRSE (1858–1925), [...]

First demonstrated by Prof Edwin Henry Barton FRS FRSE (1858–1925), Professor of Physics at University College, Nottingham, who had a particular interest in the movement and behavior of spherical bodies, the Barton's pendulums experiment demonstrates the physical phenomenon of resonance and the response of pendulums to vibration at, below and above their resonant frequencies.

In its simplest construction, approximately 10 different pendulums are hung from one common string. This system vibrates at the resonance frequency of a driver pendulum, causing the target pendulum to swing with the maximum amplitude.

The other pendulums to the side do not move as well, thus demonstrating how torquing a pendulum at its resonance frequency is most efficient. The driver pendulum should lead by pi/2 to the driven.

The driver may be a very heavy pendulum also attached to this common string; the driver is set to swing and move the whole system.Show More active

Tacoma Bridge

Collapse of the Tacoma Narrows Bridge.

Collapse of the Tacoma Narrows Bridge.

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Wine glass resonance in slow motion

Vibration and shattering of a wine glass in front of a loudspeaker. The [...]

Vibration and shattering of a wine glass in front of a loudspeaker. The tone matches the glass resonance frequency

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Amazing Resonance Experiment!

Music: Dark Wave - https://open.spotify.com/track/1gnjcZeuyHg768yZBimjRb [...]

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Tuning Fork at 1600fps - The Slow Mo Guys

A bunch of people requested a tuning fork so... BOOM! Here's a video of a [...]

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