Homework Help: Calculating Amplitude - SHM

Tags:
1. Apr 8, 2017

asteeves_

I have encountered two separate review problems that have to do with finding a value for amplitude and I am really struggling with it.

1. The problem statement, all variables and given/known data

Question 1-
A mass of 3kg is free to move on a horizontal frictionless surface and attached to a spring of k=15 N/m. It is displaced from equilibrium by 0.1m to the right and released from rest. What is the amplitude of the oscillation ?

Question 2-
A simple pendulum consists of a 4kg mass attached to a 3m long rope. At t=0 it is moving to the right at 0.4m/s. What is the maximum angle to which it swings?

2. Relevant equations

(1) x=Acos(wt+θ)
(2) v=-wAsin(wt+θ)

3. The attempt at a solution

Question 1-
I assumed the amplitude was equal to 0.1m from the question however I have a lot of trouble justifying it to myself. If this is intact the case I would really appreciate an explanation as to why, if not some insight on how to find A would be very helpful.

Question 2-
I attempted to solve for A using equation 2 and the information given regarding t=0 but ran into the issue of not knowing the value of θ, and have kind of hit a road block now.

2. Apr 8, 2017

ehild

The mass is displaced by 0.1 m to the right from equilibrium, and then released at t=0. It means that the velocity is 0 at t=0. Substitute t=0, x=0.1 and v=0 into the equations (1) and (2). What do you get for θ and A?

The pendulum moves to the right at t=0, not to the right and up, so it moves horizontally at that instant. At what angle does it move horizontally?
(You can apply also conservation of energy to get the maximum angle it swings.)

Last edited: Apr 8, 2017