A body of mass 0.1 kg performing linear SHM experiences a restoring force of 1 N when its displacement from the mean position is 5 cm. Find (i) the force constant (ii) the period of SHM (iii) the acceleration of the body, when its displacement from the mean position is 1 cm./

Explanation

Data : , m= 0.1 kg , F=1 , N x =5 `xx 10^(-2) m, x_(1) = 10^(-2) `m
(i) F= kx
The force constant = ` k = F/x = 1/(5xx 10^(-2)) = 20 ` N/m
(ii) The period of the motion
` T = 2 pi sqrt(m/k) =2pi sqrt(0.1/20) = (2pi)/(10sqrt2) = (6.284)/(14.14)`
= 0.4444 s
The magnitude of the acceleration . ltbr. ` a = omega^(2) x= ((2pi)/T)^(2) x= (4pi(10^(-2)))/(4pi^(2)//200) = 2m//s^(2)`