Question

The velocity of a particle executing SHM is 0.12 ms^-1and 0.04 ms^-1 when its displacements from the mean position are 0.01m and 0.03m respectively. Calculate the amplitude, period and maximum velocity of the particle ?

Answer 1

$$v_1=\omega \sqrt{a^2-x_1^2},v_2=\omega \sqrt{a^2-x_2^2}$$

$$\frac{v_1}{v_2}=\frac{\sqrt{a^2-x_1^2}}{\sqrt{a^2-x_2^2}}$$

$$\frac{0.12}{0.04}=\frac{\sqrt{a^2-0.01^2}}{\sqrt{a^2-0.03^2}}$$

$$a=0.032\ m$$

$$v_1=\omega \sqrt{a^2-x_1^2}\to 0.12=\omega \sqrt{0.032^2-0.01^2}$$

$$\omega=4\frac{rad}{s}$$

$$v_{max}=\omega a=(4)(0.032)=0.13\frac{m}{s}$$

$$T=\frac{2\pi}{\omega}=1.6\ s$$