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

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

Data

T = 2\pi\sqrt{\frac{L}{g}}, \quad T = 2\pi\sqrt{\frac{m}{k}}

A precision pendulum clock is designed to keep accurate time on Earth. The pendulum has a length of 0.994 m and advances one second per complete oscillation, giving a period of 2.00 s.

(a)

Determine the design value of

g

used in the clock's calibration. [2 marks]

(b)

The clock is transported to the top of a mountain where

g

decreases by 0.50%. Determine the new period of the pendulum at this location. [2 marks]

(c)

An alternative timekeeper uses a spring–mass system with mass 0.50 kg, designed to have the same 2.00 s period as the pendulum on Earth. Determine the required spring constant

k

. [2 marks]

(d)

Evaluate which timekeeper maintains more accurate timekeeping at the mountain location. Support your answer with a quantitative calculation of the timing error accumulated over one hour. [3 marks]

Solutions

2MasterySAQ-SPendulum and spring systems5 marksPaper 2~8 min

Data

g = 9.81 \text{ m s}^{-2}, \quad E_{\text{k}} = \tfrac{1}{2}mv^2, \quad E_{\text{el}} = \tfrac{1}{2}kx^2, \quad T = 2\pi\sqrt{\dfrac{l}{g}}

A mass of 0.50 kg is attached to a spring of spring constant 20 N m⁻¹ on a frictionless horizontal surface. The mass is displaced 0.12 m from its equilibrium position and released from rest. A simple pendulum, also with a bob of mass 0.50 kg, oscillates on a string of length 1.2 m with small amplitude.

(a)

State the forms of energy exchanged during one complete oscillation of each system. (i) Mass–spring system. [1]
(ii) Pendulum system. [1 mark]

(b)

Calculate the maximum speed of the mass in the mass–spring system. [2 marks]

(c)

Evaluate the effect on the period of the pendulum when the string length is halved to 0.60 m and the bob mass is doubled to 1.0 kg. [2 marks]

Solutions

3MasterySAQ-SPendulum and spring systems6 marksPaper 2~9 min

A student investigates the oscillation of a pendulum and a mass–spring system. The pendulum consists of a bob of mass

0.25 \text{ kg}

suspended from a light string of length

0.80 \text{ m}

. The mass–spring system consists of the same

0.25 \text{ kg}

mass attached to a spring of spring constant

12 \text{ N m}^{-1}

. Both systems undergo small-amplitude oscillations.

g = 9.81 \text{ m s}^{-2}, \quad T_{\text{pendulum}} = 2\pi \sqrt{\frac{l}{g}}, \quad T_{\text{spring}} = 2\pi \sqrt{\frac{m}{k}}

(a)

State two conditions required for a system to undergo simple harmonic motion. [2 marks]

(b)

Calculate the period of oscillation of the pendulum. [1 mark]

(c)

Calculate the period of the mass–spring system. [1 mark]

(d)

The student claims that changing the mass to

0.50 \text{ kg}

would make the two periods equal. Evaluate this claim by considering how each period depends on mass. [2 marks]

Solutions

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