Questions
The displacement of an object attached to a spring and executing simple harmonic motion is given by . The time at which the maximum speed first occurs is
detailed solution
Correct option is A
Given displacement x=2×10-2cos(πt) differentiate above equation with respect to time velocity =v=dxdt=−2×10−2πsin(πt) For the first time when V=Vmax velocity is maximum when sinπt=1=sin π2 πt= π2 t=12=0.5second***Alternate solution: The given equation shows that the particle is at extreme position . since πt=ω ⇒πt=2πT time period is equal to 2 sec and the particle will take a time equal to T4=0.5sec to reach the mean position where the velocity is maximum.Talk to our academic expert!
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An ideal spring with spring-constant K is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is
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