Question

A body oscillates with SHM, accroding to the equation, `x=(5.0m)cos[(2pirads^(-1))t+pi//4]`
At `t=1.5s`, calculate the `(a)` diplacement `(b)` speed and `(c)` acceleration of the body.

Answer 1

The angular frequency `omega` of the body `=2pi "rad"s^(-1)` and its time period, T=1 s.
At t=1.5 s,
(i) Displacement `=(5 m)"cos"[2pi "rad"s^(-1))xx1.5 s+pi//4]`
`" "=(5m)"cos[(3pi+pi//4)"rad"]`
`" "=-5 xx 0.707 m=-3.535 m`
(ii) Using `v=-omegaa"sin" (omegat+phi),`
Speed of the body
`" "=-(5m)(2pis^(1))"sin"[(2pis^(-1))xx1.5 s+(pi)/(4)]`
`" "=-(5m)(2pis^(-1))"sin"[(3pi+(pi)/(4))]`
`" "=10pixx 0.707 ms^(-1)=22ms^(-1)`.
(iii) Acceleration of the body
`" "-(2pi "rads"^(-1))^(2)xx"displacement"`
`" "=-(2pi "rads"^(-1))^(2)xx(-3.535 m)`
`" " =139.56 ms^(-2)`