First slide

Simple harmonic motion

Question

The piston in the cylinder head of a locomotive has a stroke of 6 m. If the piston executing simple harmonic motion with an angular frequency of 200 rad min^-1, its maximum speed is

Moderate

A

5 ms^-1
B

10 ms^-1
C

15 ms^-1
D

20 ms^-1

Solution

Here, $ω = 200 rad \min^{- 1}$
Stroke means twice the amplitude.
$∴ A = 3 m$
Maximum speed,
$v_{max} = Aω = 3 \times 200 = 600 m \min^{- 1} = \frac{600}{60} {ms}^{- 1} = 10 {ms}^{- 1}$

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