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CAIE A-Level Physics 17 Oscillations

Practise interpreting simple harmonic motion through displacement, velocity and acceleration relationships, energy changes, damping behaviour and resonance response.

Syllabus
2028–2030
Course
Physics 9702
Level
A2

Exam points

  • use SHM parameters, equations and graphs to analyse displacement, velocity, acceleration and phase
  • calculate and interpret energy interchange and total energy in SHM
  • analyse damping and resonance using amplitude, natural frequency and response graphs

Covered syllabus points

17.1 Simple harmonic oscillations17.2 Energy in simple harmonic motion17.3 Damped and forced oscillations, resonance

17. Oscillations question 1

[Maximum number: 10]

A spring is hung vertically from a fixed point. A mass M is hung from the other end of the spring, as illustrated in Fig. 3.1.

Fig. 3.1

Fig. 3.1

The mass is displaced downwards and then released. The subsequent motion of the mass is simple harmonic.

The variation with time t of the length L of the spring is shown in Fig. 3.2.

Fig. 3.2

Fig. 3.2

Question (a)

(a)

State:

[ 2 ]

Question (i)

(i)

one time at which the mass is moving with maximum speed
time =

[ 1 ]

Question (ii)

(ii)

one time at which the spring has maximum elastic potential energy.
time = s

[ 1 ]

Question (b)

(b)

Use data from Fig. 3.2 to determine, for the motion of the mass:

[ 6 ]

Question (i)

(i)

the angular frequency ω\omegaω=\omega=rads−1\mathrm{rads}^{-1}

[ 2 ]

Question (ii)

(ii)

the maximum speed
maximum speed = ms−1\mathrm{ms}^{-1}

[ 2 ]

Question (iii)

(iii)

the magnitude of the maximum acceleration.
maximum acceleration = ms−2\mathrm{ms}^{-2}

[ 2 ]

Question (c)

(c)

The mass M is now suspended from two springs, each identical to that in Fig. 3.1, as shown in Fig. 3.3.

Fig. 3.3

Fig. 3.3

Suggest and explain the change, if any, in the period of oscillation of the mass. A numerical answer is not required.

[ 2 ]

17. Oscillations question 2

[Maximum number: 8]

A small wooden block (cuboid) of mass m floats in water, as shown in Fig. 3.1.

Fig. 3.1

Fig. 3.1

The top face of the block is horizontal and has area A. The density of the water is ρ\rho.

Question (a)

(a)

The block in (b) is now released so that it oscillates vertically.

The resultant force F acting on the block is given by

F=−AgρxF=-A g \rho x

where g is the gravitational field strength and x is the vertical displacement of the block from the equilibrium position.

[ 4 ]

Question (i)

(i)

Explain why the oscillations of the block are simple harmonic.

[ 2 ]

Question (ii)

(ii)

Show that the angular frequency ω\omega of the oscillations is given by

ω=Aρgm.\omega=\sqrt{\frac{A \rho g}{m}} .
[ 2 ]

Question (b)

(b)

The block is now placed in a liquid with a greater density. The block is displaced and released so that it oscillates vertically. The variation with displacement x of the acceleration a of the block is measured for the first half oscillation, as shown in Fig. 3.3.

Fig. 3.3

Fig. 3.3

[ 4 ]

Question (i)

(i)

Explain why the maximum negative displacement of the block is not equal to its maximum positive displacement.

[ 1 ]

Question (ii)

(ii)

The mass of the block is 0.57 kg .

Use Fig. 3.3 to determine the decrease ΔE\Delta E in energy of the oscillation for the first half oscillation.
E= J

[ 3 ]
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