Question

A block is resting on a piston which executes simple harmonic motion in vertical plain with a period of 2.0 s in vertical plane at an amplitude just sufficient for the block to separate from the piston. The maximum velocity of the piston is
A. \[\dfrac{5}{\pi }m/s\]
B. \[\dfrac{10}{\pi }m/s\]
C. \[\dfrac{\pi }{2}m/s\]
D. \[\dfrac{20}{\pi }m/s\]

Answer 1

Hint: In any SHM, there consistently exists a reestablishing force which attempts to take the object back to mean position. This force causes speeding up in the object.

Complete step-by-step answer:
The correct answer is B.

Subsequently \[F=-kx\] Here F is the reestablishing force, x is the relocation of the object from the mean position, and k is the force per unit dislodging. The negative sign shows that force is inverse to the relocation. At exactly that point can the object be brought back after relocation.
\[{{a}_{\max }}=g\]
\[~{{\omega }^{2}}A=g\]
\[A=\dfrac{g}{~{{\omega }^{2}}}\]
\[mg=N+m.{{a}_{\max }}\]
\[g={{a}_{\max }}\]
\[a{{\omega }^{2}}=g\]
\[a=\dfrac{10}{{{\pi }^{2}}}m\]
\[{{V}_{MAX}}=a.\omega \]
\[=\dfrac{10}{{{\pi }^{2}}}.\dfrac{2\pi }{2}=\dfrac{10}{\pi }m/s\]
Simple harmonic motion can fill in as a numerical example for an assortment of the motions, yet is epitomized by the swaying of a mass on a spring when it is dependent upon the direct versatile reestablishing force given by Hooke's law.
The motion is sinusoidal in the time and exhibits a solitary full recurrence. Other marvels can be demonstrated by the simple harmonic motion, including the motion of a simple pendulum, in spite of the fact that for it to be a precise example, the net force on the object toward the finish of the pendulum must be corresponding to the removal (and all things being equal, it is just a decent guess when the point of the swing is little; see little edge estimate).
Simple harmonic motion can likewise be utilized to demonstrate subatomic vibration as well.

Note: If the genuine space and stage space outline are not co-straight, the stage space motion gets circular. The region encased relies upon the abundancy and the most extreme momentum.