# Vibrations and Waves: Mass on Incline problem

1. Apr 20, 2010

### huybinhs

1. The problem statement, all variables and given/known data
A spring, of negligible mass and which obeys Hooke's Law, supports a mass M on an incline which has negligible friction. The figure below shows the system with mass M in its equilibrium position. The spring is attached to a fixed support at P. The spring in its relaxed state is also illustrated.
http://i995.photobucket.com/albums/af79/huybinhs/plot-2.png

a) Mass M has a value of 245 g. Calculate k, the spring constant.

b) The mass oscillates when given a small displacement from its equilibrium position along the incline. Calculate the oscillation frequency.

2. The attempt at a solution

I know that I need to find the component of the acceleration due to gravity along the inclined plane. From the graph I can find the sinθ. Then find the force which pulls the spring down. Find the extension of the spring and then k.
But I dont know how to get started (no ideas how to get numbers on the graph). Please be a guider! Thanks!

2. Apr 20, 2010

### rl.bhat

Length of the unstretched spring is 40 cm.
Length of the stretched spring is 50*sqrt(2) cm.

3. Apr 20, 2010

### huybinhs

Thanks!
So, I got the length of the stretched spring is 70.7 cm.
In order to find k, I need to find F.
F = -mgsin(theta)
then I need to find sin(theta) first.
Could u let me know how to find sin(theta)?

4. Apr 20, 2010

### rl.bhat

sinθ = opposite side/ hypotenuse.
From the graph find these values.

5. Apr 20, 2010

### huybinhs

Hypotenuse = sqrt[60^2+60^2] = sqrt7200 = 84.85
Sin(theta) = 60/84.85 = 0.707;
F = -1.700 N. Correct?

6. Apr 20, 2010

### huybinhs

Got it all. Thanks so much rl.bhat ;)