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Question

A particle is executing simple harmonic motion, Its displacement is given by x=5 sin πt, where x is in cm and t in seconds. How long will the particle take to move from the position of equilibrium to the position of maximum displacement?

A
0.5 s
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B
1.0 s
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C
1.5 s
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D
2.0 s
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Solution

The correct option is A 0.5 s
Maximum displacement = amplitude = 5 cm
At time t = 0, x = 0 (equilibrium position). Hence time t taken by the particle to move form X = 0 to x = 5 cm is given by
5 = 5 sin π t
or, 1 = sin π t
or π t = π2 or t = 0.5s

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