Question

The equation of motion of a body of mass 20 kg in S.H.M. is $y=0.04\sin (100t+\frac{\pi }{4}).$ Then
i) Amplitude is 0.04 m
ii) Frequency is 15.92 Hz.
iii) Initial phase $\varphi =\frac{\pi }{4}$ radians.
iv) $V_{max}=4m{s}^{-1}.$
v) $a_{max}=400m{s}^{-2}.$
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

Answer 1

The correct option is C All are correct

Compare the above equation with standard equation $y=A\sin (\omega t+\varphi )$

i) Amplitude A = $0.04m$
ii) Frequency $\frac{\omega }{2\pi }=\frac{100}{2\pi }=\frac{100}{6.28}=15.92Hz.$
iii) Initial phase $\varphi =\frac{\pi }{4}$ radians.
iv) $V_{max}=\omega A=100\times 0.04=4m{s}^{-1}.$
v) $a_{max}={\omega }^{2}A={100}^2\times 0.04=400m{s}^{-2}.$
vi) Max. k.E = $\frac{1}{2}$ m $(V_{max}{)}^2=\frac{1}{2}\times 20\times 4\times 4=160J.$