Practise explaining damping, classifying light, critical and heavy damping, interpreting decay and resonance under forced oscillation.
An object is suspended from a vertical spring as shown in Fig. 3.1.
Fig. 3.1
The object is displaced vertically and then released so that it oscillates, undergoing simple harmonic motion.
Fig. 3.2 shows the variation with displacement x of the energy E of the oscillations.
Fig. 3.2
The kinetic energy, the potential energy and the total energy of the oscillations are each represented by one of the lines P, Q and R .
State the cause of damping.
State, with a reason, the type of damping that the card introduces into the system.
A heavy metal sphere of mass 0.81 kg is suspended from a string. The sphere is undergoing small oscillations from side to side, as shown in Fig. 4.1.
Fig. 4.1
The oscillations of the sphere may be considered to be simple harmonic with amplitude 0.036 m and period 3.0 s .
The suspended sphere is now lowered into water. The sphere is given a sideways displacement of +0.036 m from its equilibrium position and is then released at time t=0. The water causes the motion of the sphere to be critically damped.
On Fig. 4.2, sketch the variation of the displacement x of the sphere from its equilibrium position with t from t=0 to .
Fig. 4.2
State what is meant by resonance.
A small ball is held in place using a stretched string. One end of the string is fixed to a wall and the other end is attached to a vibration generator, as shown in Fig. 4.1.
Fig. 4.1
Initially, the vibration generator is switched off.
A student displaces the ball vertically and then releases it. Fig. 4.2 shows the variation of the displacement of the ball with time after it is released.
Fig. 4.2
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.
The vibration generator in (b) is switched on and its frequency f of vibration is gradually increased from 0 to 10 Hz .
On Fig. 4.3, sketch the variation with f of the amplitude of the oscillations of the ball.
Fig. 4.3
An object is suspended from a vertical spring as shown in Fig. 3.1.
Fig. 3.1
The object is displaced vertically and then released so that it oscillates, undergoing simple harmonic motion.
Fig. 3.2 shows the variation with displacement x of the energy E of the oscillations.
Fig. 3.2
The kinetic energy, the potential energy and the total energy of the oscillations are each represented by one of the lines P, Q and R .
State the cause of damping.