The equation of motion of a body of mass 20 kg in SHM i

| The equation of motion of a body of mass 20 kg in S.H.M. is

y = 0.04 sin (100 t + \frac{π}{4}) .

Then
i) Amplitude is 0.04 m
ii) Frequency is 15.92 Hz.
iii) Initial phase

ϕ = \frac{π}{4}

radians.
iv)

V_{m a x} = 4 m s^{- 1} .

a_{m a x} = 400 m s^{- 2} .

vi) Max. k.E = 160 J

A. 1,2 and 3 are correct

B. 1,3 and 4 are correct

C. All are correct

D. 1, 2 3 and 5 are correct

Please scroll down to see the correct answer and solution guide.

Right Answer is: C

SOLUTION

Compare the above equation with standard equation $y = A sin (ω t + ϕ)$

i) Amplitude A = $0.04 m$
ii) Frequency $\frac{ω}{2 π} = \frac{100}{2 π} = \frac{100}{6.28} = 15.92 H z .$
iii) Initial phase $ϕ = \frac{π}{4}$ radians.
iv) $V_{m a x} = ω A = 100 \times 0.04 = 4 m s^{- 1} .$
v) $a_{m a x} = ω^{2} A = 100^{2} \times 0.04 = 400 m s^{- 2} .$
vi) Max. k.E = $\frac{1}{2}$ m $(V_{m a x})^{2} = \frac{1}{2} \times 20 \times 4 \times 4 = 160 J .$

The equation of motion of a body of mass 20 kg in SHM i

Right Answer is: C

SOLUTION

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