Oscillations

Determine the amplitude of the oscillations.

amplitude = ______ $\text{m}$

State what the line in Fig. 5.2 shows about the nature of the oscillations.

State three other quantitative conclusions that can be drawn from Fig. 5.2 and Fig. 5.3 about the block and its oscillations. Use the space for any working.

On Fig. 5.4, sketch the variation with $h$ of the potential energy $E_P$ of the oscillations.

State what is meant by simple harmonic motion.

Calculate the period of the oscillation.

period = ______ $\text{s}$

Determine the amplitude $x_0$ of the oscillation.

$x_0$ = ______ $\text{m}$

Use your answer in (b)(ii) to determine the equation for $v$ in terms of the displacement $x$ of the block, where $v$ is in $\text{m s}^{-1}$ and $x$ is in $\text{m}$.

$v$ = ______

On Fig. 5.1, sketch the variation of $v$ with $x$.

Determine the amplitude of the oscillations.

amplitude = ______ $\text{m}$

State what the line in Fig. 5.2 shows about the nature of the oscillations.

State three other quantitative conclusions that can be drawn from Fig. 5.2 and Fig. 5.3 about the block and its oscillations. Use the space for any working.

On Fig. 5.4, sketch the variation with $h$ of the potential energy $E_P$ of the oscillations.

State what is meant by simple harmonic motion.

State two times at which the sphere is passing in the same direction through the equilibrium position.

time ______ and time ______

The time interval between $t_1$ and $t_6$ is $2.2\ \text{s}$.

Calculate the frequency of oscillation of the sphere.

frequency = ______ $\text{Hz}$

The sphere in (b) is undergoing simple harmonic motion.

Use your answer in (b)(ii) and data from Fig. 4.2 to determine the maximum displacement of the sphere from its equilibrium position.

maximum displacement = ______ $\text{m}$

State what is meant by damping.

Describe what is observed to indicate that the damping is light.

By reference to electromagnetic induction and to conservation of energy, explain why the oscillations are damped.

The procedure in (a) is repeated after replacing the resistor with one of greater resistance.

Suggest, with a reason, the effect of this change on the oscillations.

Explain how Fig. 5.2 shows that the oscillations of the ball are simple harmonic.

Determine the period $T$ of the oscillations.

$T$ = ______ $\text{s}$

State what is meant by damping.

On Fig. 5.3, sketch a possible variation of the displacement $x$ of the ball with $t$ between $t = 0$ and $t = 2T$.

State what is meant by the frequency of the oscillations of an oscillating object.

Explain how Fig. 4.2 shows that the period of the oscillations is $0.80\ \text{s}$.

Calculate the angular frequency $\omega$ of the oscillations.

$\omega$ = ______ $\text{rad s}^{-1}$

Apart from the period, frequency and angular frequency of the oscillations, determine three other conclusions about the object and its oscillations that may be drawn from Fig. 4.1 and Fig. 4.2. The conclusions may be qualitative or quantitative. Use the space below for any working.

1 ______

2 ______

3 ______

Describe the interchange between kinetic energy and potential energy during the oscillations. Numerical values are not required.

The total energy of the oscillations of the object is $2.2 \times 10^{-4} \text{ J}$.
In one oscillation the object travels a total distance of $14 \text{ mm}$.

Calculate the angular frequency $\omega$ of the oscillations.

$\omega$ = ______ $\text{rad s}^{-1}$

Calculate the maximum amplitude of the oscillations so the object does not lose contact with the platform.

amplitude = ______ $\text{m}$

The amplitude of the oscillations is increased so it is greater than the value in (b)(i).

State and explain the position in an oscillation where the object first loses contact with the platform.

State what is meant by resonance.

State the name of the phenomenon illustrated by the decrease in the amplitude of the oscillations in Fig. 4.2.

Explain the decrease with time of the amplitude of the oscillations of the ball.

Determine the frequency of the oscillations of the ball.

frequency = ______ $\text{Hz}$

The vibration generator in (b) is switched on and its frequency $f$ of vibration is gradually increased from 0 to $10\ \text{Hz}$.

On Fig. 4.3, sketch the variation with $f$ of the amplitude of the oscillations of the ball.

Explain how Fig. 4.2 shows that the oscillations of the block are simple harmonic.

the angular frequency $\omega$ of the oscillations

$\omega$ = ______

the maximum speed $v_0$ of the oscillations

$v_0$ = ______

the energy $E$ of the oscillations.

$E$ = ______

The period of the oscillations is $0.75\ \text{s}$ and the value of $3Y$ is $1.8\ \text{cm}$.

Determine an expression for $x$ in terms of time $t$, where $x$ is in $\text{cm}$ and $t$ is in seconds.

$x$ = ______