Question

The figure shows the position-time graph of an object of mass m oscillating on the end of a massless ideal spring of spring constant k. Answer the following questions.

x (m) 0.3 0.2 0.1 f (S) -0.1 -0.2 -0.3

1. Which of the following graphs is the correct velocity-time graph of the oscillation?

2. Which of the following graphs is the correct acceleration-time graph of the oscillation

3. If the mass of the object is m = 0.500 kg, what is the spring constant k of the ideal spring?

Hint: read o the period of the oscillation T from the graph and use the relations

4. What is the total mechanical energy of the mass-spring system?

Answer 1

This is graph of cos x(t) = A cos w t (1) rightarrow (A) rightarrow amplitude w rightarrow angular frequency speed u = dx/ dt = d/dt = (A cos wt) u = -A w sin wt rightarrow (ii) from graph = A = 0.2 m time period T = pi second Then w = 2 pi/ T = 2 pi/ pi sec = 2 sec-1 part 1: putting value of 'A' & 'w' in eqn (ii) we get v = -0.2m times 2sec^-1 sin (2s^-1) t v = -0.4 m/s sin (2 s^-1 t) \r\n velocity graphs is missing match the graph i have drawn. Part 2: Accelerate a = dv/ dt a = d/dt (- A w sin dt) a = -A w^2 cos wt pitting the values of 'n' & 'w' , we get Acceleration 'a' = -0.2 m times (2s)^2 cos wt = -0.8 m/s^2 sin w t graph of