Question

The amplitude of a body executing shm is 2 cm. Its mass is 20 g and the frequency of vibration is
20 Hz. Find its (i) maximum velocity (ii) energy ?

Answer 1

Answer:

i)maximum velocity= 40 cm/sec

ii) energy=16000 erg

Answer 2

Given,

Mass= 20g= 20×$10^{-3}$ kg

amplitude = 2cm

frequency = 2Hz

To Find,

1) maximum velocity

2) energy

Solution,

Since frequency is given we can find the angular frequency,ω

                ω = 2πf

                    =40π

1)Maximum velocity, $V_{max}$ = Aω

                                          = 2cm × 40π

                                          = 80π cm/s

2)Energy, E= $\frac{1}{2} mV_{max} ^{2}$

                    =$\frac{1}{2}$×20×$10^{-3}$×($\frac{80\pi }{100}$ m/s)²

                    =6.3 × $10^{-2}$ J

∴ Hence, the maximum velocity is 80π cm/s and the energy is 6.3 × $10^{-2}$ J.