A block of mass m 01 kg is hung from a spring whose force c

A block of mass m = 0.1 kg is hung from a spring whose force constant is k = 40N/m. The damping force on the block is given by F_d = - gamma v, where ?=0.2N-s/m. The mass is subject to an oscillatory driving force of F=F_0 cos omega t, where F_0 =1.6N. What are the resonant frequency the damping constant gamma, and the Q of the system? [Ans:omega_0 =20 radians/s, gamma =2s^-1, Q =10] What is the amplitude of oscillation at the resonant frequency? [Ans: 0.4m] (c) At what frequency is the amplitude of oscillation equal to its maximum value? [19.95 radians/s] (d) At what frequencies is the amplitude of oscillation half of its maximum value? [Ans:21.73 and 18.27 radians/s] (e) What are the limiting amplitudes of oscillation for w much less than and much greater than resonant frequency? |[Ans: A(0) = 0.04m, A(omega rightarrow infinity) = 16/omega^2 m] (f) What are the phase and time differences between the displacement and the force at omega = omega_0, omega = 2omega_0? [Ans: phi= pi/2, =0.079 s; phi =0.067 radians, delta t =6.7 times 10^-3 s; phi =3.075 radians; delta t =0.077 s]

Solution

Ans1 20.04 radian/sec , Q= 8.97

Ans 2 =.389m.

Ans 3 = 17 radian /sec

Ans4= .4 , infinity, 16 omega square.