IB Physics SL C.1.4 Period, Frequency and Angular Frequency

Practise converting T, f and ω and applying spring or pendulum period relations to predict how mass, stiffness, length or gravitational field changes an oscillator's timing.

Exam points

convert between T, f and ω with T = 1/f = 2π/ω and retain seconds, hertz or rad s⁻¹
use T = 2π√(m/k) to compare spring systems after mass or effective stiffness changes
use T = 2π√(L/g) for small-angle pendulums and identify variables that do not affect period

[Maximum number: 3]

This question is in two parts. Part 1 is about ideal gases and specific heat capacity. Part 2 is about simple harmonic motion and waves.
Part 1 Ideal gases and specific heat capacity

Simple harmonic motion and waves

One end of a light spring is attached to a rigid horizontal support.

Figure for Question C.1.4—Period, frequency and angular frequency question 1 — IB Physics SL

An object W of mass 0.15 kg is suspended from the other end of the spring. The extension x of the spring is proportional to the force F causing the extension. The force per unit extension of the spring k is $18 \mathrm{Nm}^{-1}$ .

A student pulls W down such that the extension of the spring increases by 0.040 m . The student releases W and as a result W performs simple harmonic motion (SHM).

Determine the period of oscillation of the spring.

$\omega=\sqrt{\frac{a}{x}}$ ;
$=10.95 \mathrm{rads}^{-2}$ ;

T=\left(\frac{2 \pi}{\omega}=\right) \frac{6.28}{10.95}=0.57 \mathrm{~s} ;

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C.1.4—Period, frequency and angular frequency question 1