Answer to Question #282288 in Physics for varaprasad

Question

2. A spring-mass system consisting of m = 2 kg and spring constant k = 50N/m is executing simple harmonic motion with amplitude of 0.9 m. (a) Calculate the total mechanical energy of the oscillator (b) What is the maximum velocity of the mass (c) For what value(s) of displacement will the oscillator have maximum kinetic energy ? (d) For what value(s) of displacement will the oscillator have maximum potential energy ? (e) If the oscillator is subjected to a mild damping force b= 0.07 kg/s find the time constant for the damped oscillator. 

Answer 1

(a) The total mechanical energy of the oscillator:

$$E=\frac12kx^2=20.3\text{ J}.$$

(b) The maximum velocity of the mass:

$$v=x\sqrt{k/m}=0.45\text{ m/s}.$$

(c) The oscillator has the maximum kinetic energy at the point of equilibrium (zero displacement compared to the resting state of the mass just hanging on the spring).

(d) The potential energy is at the maximum when the mass is at the maximum displacement.

(e) The time constant is

$$\tau=\frac{2m}b=57\text{ s}.$$