Question

A body vibrating with simple harmonic motion has a frequency of 4Hz and an amplitude of 0.15m. Calculate the maximum values of the acceleration and velocity. Calculate the acceleration and velocity at a point 0.09m from the equilibrium position of motion

Answer 1

$$a_m=A(2\pi f)^2=0.15(2\pi(4))^2=94.7\frac{m}{s^2}$$

$$v_m=A(2\pi f)=0.15(2\pi(4))=3.77\frac{m}{s}$$

$$a=x(2\pi f)^2=0.09(2\pi(4))^2=56.8\frac{m}{s^2}$$

$$v=\sqrt{A^2-x^2}(2\pi f)=\sqrt{0.15^2-0.09^2}(2\pi(4))=3.02\frac{m}{s}$$