IB Physics SL C.1 Simple harmonic motion questions

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Question 1

Multiple choiceMedium1 mark

An ideal mass–spring system has mass $m$ spring constant $k$ and angular frequency $\omega$ The mass is changed to $m/4$ and the spring constant to $9k$ What is the ratio of the new angular frequency to $\omega$

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Answer: D. For a mass–spring system, $T=2\pi\sqrt{m/k}$ and $\omega=2\pi/T$

\frac{T_{\text{new}}}{T} =\sqrt{\frac{(m/4)/(9k)}{m/k}} =\frac{1}{6}, \qquad \frac{\omega_{\text{new}}}{\omega} =\frac{T}{T_{\text{new}}} =6.

A: gives the period ratio but does not take its reciprocal for angular frequency.
B: applies the mass change alone, giving a factor of $2$ and omits the spring change.
C: applies the spring change alone, giving a factor of $3$ and omits the mass change.
Remember: combine both changes when finding the period, then use the inverse relation between angular frequency and period.

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