Sure! Below are five sample questions related to Simple Harmonic Motion (SHM) that reflect the style and topics typically covered in WAEC, NECO, and GCE examinations, along with their answers.
Sample Questions on Simple Harmonic Motion
Question 1
A mass attached to a spring oscillates with an amplitude of 0.1 m. If the spring constant is 200 N/m, what is the maximum speed of the mass during its oscillation?
Answer:
The maximum speed \( v_{max} \) in Simple Harmonic Motion can be calculated using the formula:
\[
v_{max} = A \sqrt{\frac{k}{m}}
\]
However, without the mass \( m \), we cannot solve directly. Assuming \( m \) is known, rearrange or substitute known values to find \( v_{max} \).
Question 2
A pendulum makes 50 oscillations in 80 seconds. What is the period of the pendulum?
Answer:
The period \( T \) is given by:
\[
T = \frac{\text{Total time}}{\text{Number of oscillations}} = \frac{80 \text{ s}}{50} = 1.6 \text{ s}
\]
Question 3
If a simple harmonic oscillator has a period of 2 seconds, what is the frequency of the oscillator?
Answer:
The frequency \( f \) is given by:
\[
f = \frac{1}{T} = \frac{1}{2 \text{ s}} = 0.5 \text{ Hz}
\]
Question 4
A body moves in SHM with an amplitude of 0.3 m and a maximum speed of 2 m/s. What is the angular frequency of the motion?
Answer:
The angular frequency \( \omega \) can be calculated using:
\[
v_{max} = A \omega \implies \omega = \frac{v_{max}}{A} = \frac{2 \text{ m/s}}{0.3 \text{ m}} \approx 6.67 \text{ rad/s}
\]
Question 5
A harmonic oscillator has a displacement given by \( x(t) = 0.2 \cos(5t) \). What is the time period of the motion?
Answer:
The general form of SHM displacement is \( x(t) = A \cos(\omega t) \). Here, \( \omega = 5 \) rad/s. The time period \( T \) is given by:
\[
T = \frac{2\pi}{\omega} = \frac{2\pi}{5} \approx 1.26 \text{ s}
\]
Feel free to use these questions and answers for study or practice.
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