Question #276932

​1 kg block vibrates in shm with amplitude of 15 cm and period of T = 2 s find the frequency, its maximum speed and its speed

when the displacement is 5cm, its maximum acceleration when the displacement is 5cm.

 


1
Expert's answer
2021-12-09T09:22:45-0500

Frequency:


f=1T=0.5 Hz.f=\frac 1T=0.5\text{ Hz}.

Maximum speed:


vmax=2πfA=0.47 m/s.v_\text{max}=2\pi fA=0.47\text{ m/s}.


Speed at x=5 cm:


x(t)=5=15cos(2πft),t=0.39 s,v=vmaxsin(2πft)=0.44 m/s.x(t)=5=15\cos(2\pi ft),\\ t=0.39\text{ s},\\ v=-v_\text{max}\sin(2\pi ft)=0.44\text{ m/s}.

Acceleration when the displacement is 5 cm:


a=(2πf)2Asin(2πft)=1.39 m/s2.a=-(2\pi f)^2A\sin(2\pi ft)=-1.39\text{ m/s}^2.


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