A simple pendulum of length 40 cm oscillates with an angular amplitude of 0.04 rad. Find a. the time period b. the linear amplitude of the bob, c. The speed of the bob when the strig makes 0.02 rad with the vertical and d. the angular acceleration when the bob is in moemntary rest. Take `g=10 ms^-2`.

Explanation

(a) `T=2pisqrt(L/g)=2pisqrt((0.4)/(10))=1.26s`
`omega=sqrt(g//L)=sqrt(10//0.4)=5rad//s`
(b)
Linear amplitude `a=Ltheta_0=40xx0.04=1.6cm`.
(c) `omega^'=omegasqrt(theta_0^2-theta^2)`
`=5sqrt((0.04)^2-(0.02)^2)`
`=0.17rad//s`
(d) `alpha=omega^2theta_0=(5)^2(0.04)`
`=1rad//s^2`
[In extreme position, angular velocity `omega^'=0`]