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Simple Harmonic Motion · Paper 2 — Free Physics HL Practice Questions

1FoundationSAQ-LPendulum and spring systems9 marksPaper 2~14 min

A spring-mass system oscillates with a period of 0.60 s when a 0.25 kg mass is attached. Separately, a simple pendulum of length 1.50 m is set into motion with small amplitude on Earth.

T = 2\pi\sqrt{\frac{m}{k}}, \quad T = 2\pi\sqrt{\frac{L}{g}}, \quad g = 9.81 \text{ m s}^{-2}

(a)

Determine the spring constant

k

of the spring. [2 marks]

(b)

Determine the period of the pendulum on Earth. [2 marks]

(c)

The pendulum is taken to a planet where the gravitational field strength is half that of Earth. Determine the new period of the pendulum on this planet. [2 marks]

(d)

Explain why the period of the spring-mass system would remain unchanged on the planet in (c). [2] (e) A spacecraft undergoes variable acceleration during flight. Evaluate which system — the spring-mass oscillator or the pendulum — would be more reliable for timekeeping aboard the spacecraft. [3 marks]

Solutions

2FoundationSAQ-SDisplacement, velocity, and acceleration in SHM4 marksPaper 2~6 min

A mass-spring system oscillates with simple harmonic motion. The displacement of the mass from its equilibrium position is given by

x = 0.032\cos(4.5t)

, where

x

is in metres and

t

is in seconds.

(a)

State two characteristics of the acceleration of a mass undergoing simple harmonic motion. [2 marks]

(b)

Calculate the magnitude of the maximum acceleration of the mass. [2 marks]

Solutions

3MasterySAQ-SDisplacement, velocity, and acceleration in SHM5 marksPaper 2~8 min

A loudspeaker cone oscillates with simple harmonic motion. The cone has an amplitude of

2.5\,\text{mm}

and a frequency of

120\,\text{Hz}

. At time

t = 0

, the cone is at its maximum positive displacement.

(a)

State the acceleration of the cone at the instant it passes through the equilibrium position. [1 mark]

(b)

Calculate the magnitude of the maximum acceleration of the cone. [2 marks]

(c)

The cone passes through the equilibrium position with maximum speed. Using energy conservation, explain why the speed is maximum at this point and not any other displacement. [2 marks]

Solutions

4ChallengeSAQ-LPendulum and spring systems7 marksPaper 2~11 min

A pendulum consists of a small metal bob of mass

m = 0.200 \text{ kg}

attached to a light string of length

L = 1.50 \text{ m}

. It is displaced by a small angle and released from rest. The pendulum is inside an elevator accelerating upward at

a = 2.00 \text{ m s}^{-2}

(a)

Determine the effective gravitational acceleration

g_{\text{eff}}

experienced by the pendulum bob in the accelerating elevator. [1 mark]

(b)

Determine the period of the pendulum in the accelerating elevator. [2 marks]

(c)

The bob is detached from the string and attached instead to a vertical spring of spring constant

k = 50.0 \text{ N m}^{-1}

. Calculate the period of oscillation of this spring–mass system inside the same accelerating elevator. [1 mark]

(d)

Explain why the period of the spring–mass system is unaffected by the elevator's acceleration, whereas the period of the pendulum is affected. Hence deduce which system would function as a more reliable clock in a non-inertial reference frame, and justify your answer. [3 marks]

Solutions

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