First slide

Simple hormonic motion

Question

A particle is executing a motion in which its displacement as a function of time is given by
$x = 3 \sin (5 πt + \frac{π}{3}) + \cos (5 πt + \frac{π}{3})$ where x is in m and t is in s. Then the motion is

Moderate

A

simple harmonic with time period 0.2 s
B

simple harmonic with time period 0.4 s
C

simple harmonic with amplitude 3 m
D

not a simple harmonic but a periodic motion

Solution

$x = 3 \sin (5 πt + \frac{π}{3}) + \cos (5 πt + \frac{π}{3})$
Amplitude = $x_{m a x} = \sqrt{3^{2} + 1^{2}} = \sqrt{10}, ω = 5 π$
$T = \frac{2 π}{ω} = \frac{2 π}{5 π} = 0.4 s$

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