Question

A horizontal spring of spring constant k = 125N/m is resting at its equilibrium length. One end of the spring is attached to a wall, and the other end is attached to a mass M = 200g. The whole system is immersed in a viscous fluid with linear drag coefficient b = 0.1 kg/s. The mass is pulled 10cm from its equilibrium position and released from rest.

1. (a) (0.5 pt) What would be the oscillation period if the system were NOT immersed in a fluid and there was no damping?

2. (b) (1 pt) Show that the mass will still undergo oscillations in the fluid (i.e. show that the motion is underdamped).

3. (c) (1.5 pts) By what factor does the period increase when the oscillator is immersed in the fluid? In other words, find T/T0 where T is the oscillation period in the fluid, and T0 is the oscillation period if there were no fluid. Hint: derive an algebraic formula for T/T0 before plugging in any numbers.

4. (d) (0.5 pt) What is the amplitude of the oscillation at t = 10 seconds?

5. (e) (1.5 pt) Recall that the total mechanical energy of a mass on a spring is E = kA2/2 where A is the amplitude of the oscillation. How many oscillations will the mass have completed before it loses half of its initial energy? [Your answer does not need to be an integer.]

6. (f) (1 pt) Suppse now you change the mass M to a different value, but all other conditions remain the same. What is the smallest mass m which will undergo any oscillations at all in this fluid?

Answer 1

Sol i Given k 125 N M: 2000.2 No.2 25 Bad sec gad l sec . 25 To: 2513 sec 6- EN 21125 2 0.01-4 (So-systeer . s-underdamped C: 24.9987 5adse リー 27T 0 100005

Lo a X sin Xo 100005 YLo.000500 L 005 10:00 05 e-go L Sin( 24.9984-ttMa) X (Jo)--10.0005 e