Question

A 100 g mass vibrates horizontally without friction at the end of an horizontal spring for which the spring constant is 10 N/m. The mass is displaced 0.5 cm from its equilibrium and released. Find: (a) Its maximum speed, (b) Its speed when it is 0.3 cm from equilibrium. (c) What is its acceleration in each of these cases?

Answer 1

(a) \(\omega=\sqrt{k/m}=\sqrt{10/0.1}\)

\(=10\,s^{-1}\) and A = 0.005 m

The maximum speed \(=A\omega\) = 0.05 m/s

(b) \(|\nu|=\omega\sqrt{A^2-x^2}\)

\(=10\sqrt{(0.005)^2-(0.003)^2}\)

.\(=10\sqrt{\frac{8\times2}{10^6}}\)

\(=10\times\frac4{10^3}=\frac4{100}\)

= 0.04 m/s

(c) Acceleration a \(=-\omega x\)

(i) At x = 0, a = 0

(ii) At x = 0.3 cm, \(a=-0.03\,m/s^2\)