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IB Physics: Simple harmonic motion — Practice Questions & Answers
92 practice questions available for this topic — here are 10 with full answers and explanations.
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Practice questions with answers
1
Multiple choice · Medium
The period of a simple pendulum of length $l$ (for small swings) is given by:
- $T=2\pi\sqrt{\frac{l}{g}}$
- $T=2\pi\sqrt{\frac{g}{l}}$
- $T=2\pi\frac{l}{g}$
- $T=2\pi\sqrt{lg}$
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WhyFor small amplitudes $T=2\pi\sqrt{\frac{l}{g}}$; the period depends on length and $g$, not on the mass or amplitude.
2
Multiple choice · Medium
A mass $m$ on a spring of stiffness $k$ oscillates with period:
- $T=2\pi\sqrt{\frac{m}{k}}$
- $T=2\pi\sqrt{\frac{k}{m}}$
- $T=2\pi\frac{m}{k}$
- $T=2\pi mk$
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WhyFor a mass-spring system $T=2\pi\sqrt{\frac{m}{k}}$.
3
Multiple choice · Easy
The frequency $f$ and period $T$ of an oscillation are related by:
- $f=\frac{1}{T}$
- $f=T$
- $f=2\pi T$
- $f=T^{2}$
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WhyFrequency is the reciprocal of period: $f=\frac{1}{T}$.
4
Multiple choice · Medium
A defining feature of simple harmonic motion is that the acceleration is:
- Proportional to displacement and oppositely directed
- Constant in magnitude and direction
- Proportional to velocity
- Always directed away from equilibrium
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WhyIn SHM the acceleration is proportional to the displacement from equilibrium and directed opposite to it: $a\propto -x$.
5
Multiple choice · Hard
For a simple pendulum undergoing small oscillations, increasing the amplitude slightly will:
- Leave the period essentially unchanged
- Double the period
- Halve the period
- Make the period zero
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WhyFor small angles the period is independent of amplitude (isochronous), so the period is essentially unchanged.
6
Multiple choice · Medium
At which point in its oscillation does an SHM oscillator have maximum speed?
- At the equilibrium position
- At maximum displacement
- Halfway between equilibrium and amplitude
- At the turning points
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WhySpeed is greatest at the equilibrium position, where all the energy is kinetic and displacement is zero.
7
Fill in the blank · Easy
In simple harmonic motion the acceleration is always directed toward the position.
Answer:
equilibrium / rest / central
WhyThe restoring force, and hence the acceleration, always points back toward equilibrium.
8
Fill in the blank · Medium
A pendulum has a period of $2.0\,\text{s}$. Its frequency is $\text{Hz}$.
Answer:
0.5 / 0.50
Why$f=\frac{1}{T}=\frac{1}{2.0}=0.50\,\text{Hz}$.
9
Multiple choice · Medium
A mass oscillates on an ideal spring with simple harmonic motion. Which statement about the energy of the system is correct?
- The maximum kinetic energy equals the maximum elastic potential energy
- The kinetic energy is largest at the amplitude
- The potential energy is constant throughout the motion
- The total energy is zero at the equilibrium position
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WhyIn SHM with no damping the total energy is constant; the maximum kinetic energy equals the maximum elastic potential energy.
10
Multiple choice · Easy
During SHM, at the equilibrium position the energy of the oscillator is
- entirely kinetic
- entirely potential
- zero
- split equally between kinetic and potential
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WhyAt equilibrium displacement is zero, so potential energy is zero and the energy is entirely kinetic.
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