SHM 3

SHM 3

When a body oscillates with SHM, at any point along its path the total energy of the body is equal to the sum of the kinetic and potential energy of the body

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For a mass oscillating on a spring with SHM the graph shows how the kinetic and potential energies vary with time, but they always add up to the _____ energy  $\frac{1}{2}kA^2$  
Notice in this case that at time zero we can tell ________ was zero since kinetic energy started at zero while potential energy was maximum.

Multiple Choice

The correct displacement equation for this motion is:

• $y=A\cos\omega t$

• $y=A\sin\omega t$

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In many every day examples SHM systems tend to lose energy to heat due to ________. This has no effect on the period of motion but it means the maximum ____________ is reduced as the oscillations proceed.

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Damping can be useful. Shock absorbers in motor vehicles are designed to ____ the oscillations of the suspension springs. If the shocks become worn out, the vehicle will bounce up and down ____ when travelling over bumpy roads.

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Applying a varying force to an object free to move can cause it to oscillate with SHM. This is called forced SHM.

The amplitude of the forced motion depends on how closely the natural frequency matches the frequency of the driving force. When the two frequencies are equal the resulting amplitude is very large and we call this _________.

Of course the more _______ the less affect the driving force will have so the smaller the resonance will be.

Multiple Select

An opera singer sings a high note and holds it for long enough that a crystal glass suddenly shatters.

Select all true statements.

• the damping was high

• the damping was low

• the sound vibrations matched the natural frequency of the crystal glass

• resonance of the crystal glass occurred

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Examples of useful resonance:

* Microwave ovens : water molecules in food resonate at particular frequencies causing the food to ____

* Tuning circuits : in TVs and radios LCR circuits resonate at particular frequencies to receive broadcasts

*Digital timers : time is maintained by __________ quartz crystals

Multiple Choice

A spring oscillates with an amplitude of 0.20 m and a period of 1.5 s. The total energy of the spring is 10 J. After 5 cycles of SHM the amplitude has reduced to 0.10 m. What is the period of oscillation after 5 cycles?

• 1.5 s

• 0.75 s

• 1.14 s

• 1.0 s

Multiple Choice

A spring oscillates with an amplitude of 0.20 m and a period of 1.5 m. The total energy of the spring is 10 J. After 5 cycles of SHM the amplitude has reduced to 0.10 m. What is the total energy of the spring after 5 cycles?

• 2.5 J

• 5.0 J

• 10 J

• 6.7 J