A body describe simple harmonic motion with an amplitude of 5 cm and a period of `0.2 s.` Find the acceleration and velocity of the body when the displacement is (a) 5 cm (b) 3 cm (c ) 0 cm.

Explanation

Given that, `A=5 cm=5xx10^(-2)m and T=0.2s`
Angular velocity, `omega=(2pi)/(T)=(2pi)/(0.2)=10pi` rad `s^(-1)`
a) Displacement, `y=5cm=5xx10^(-2)m` ,
i) Acceleration of the body, `a=-omega^(2)y`
`=-(10pi)^(2)xx5xx10^(-2)=-5pi^(2)ms^(-2)`
ii) Velocity of the body, `v=omegasqrt(A^(2)-y^(2))`
`=10pisqrt((5xx10^(-2))-(5xx-10^(-2))^(2))=0`
b) Displacement, `y=3cm=3xx10^(-2)m`
i) Acceleration of the body, `a=-omega^(2)y`
`=-(10pi)^(2)xx3xx10^(-2)m`
ii) Velocity of the body, `v=omegasqrt(A^(2)-y^(2))`
`=10pisqrt((5xx10^(-2))^(2)-(3xx10^(-2))^(2))`
`=10pixx4xx10^(-2)=0.4pi ms^(-1)`
c) Displacement, `y=0 cm`
i) Acceleration of the body, `a=-omega^(2)y=0`
ii) Velocity of the body, `v=omegasqrt(A^(2)-y^(2))`
`10pisqrt((5xx10^(-2))^(2)-(3xx10^(-2))^(2))`
`=10pixx5xx10^(-2)=0.5pi ms^(-1)`