Question

For a system shown in the figure the block has mass 1.5 kg & spring constant 8.0 N/m.Suppose the block is pulled down a distance 12 c.m & released.If the friction of force is given by -bv where b=0.23 kg/s.find the number of oscillation made by the block during the time interval required for amplitude to fall to 1/3 of initial value

Answer 1

$$\omega_0=\sqrt{\frac{k}{m}-\left(\frac{b}{2m}\right)^2}$$

$$F \backsim A^2$$

If amplitude gets reduced to one third the force will reduce to one nineth.

$$F \backsim a \backsim \omega^2$$

$$t=\frac{2(3)\pi}{\omega_0}=\frac{2(3)\pi}{\sqrt{\frac{k}{m}-\left(\frac{b}{2m}\right)^2}}$$

$$t=\frac{2(3)\pi}{\sqrt{\frac{8}{1.5}-\left(\frac{0.23}{2(1.5)}\right)^2}}=8.2\ s$$