A piston executes SHM in a cylinder according to the displacement function x(t)=0.10…

PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics

Problem

A piston executes SHM in a cylinder according to the displacement function

x(t)=0.10\cos(8\pi t)\text{ m}

where

t

is in seconds and

x

is measured from equilibrium. (a) Calculate the period

T

of the motion. (b) Determine the smallest positive time

t

(in s) at which the piston passes through the equilibrium position moving toward negative

x

. (c) Determine the smallest positive time

t

at which the piston’s velocity is zero after

t=0

. (d) Determine the smallest positive time

t

at which the piston’s acceleration attains its most negative value.