Calculating amplitude after 50 oscillations

[marshall104]

Homework Statement

An oscillator with a mass of 600 g and a period of 1.20 s has an amplitude that decreases by 2.50% during each complete oscillation. If the initial amplitude is 6.40 cm, what will be the amplitude after 50.0 oscillations?

Homework Equations

How do I approach this problem. I am so confused

Ive been using xmax=Ae(-t/2x)

with no luck. any help would be great

The Attempt at a Solution

m=600g
T=1.2s
amplitude decreases by 2.5%
I think my problem is I don't understand were xmax is coming from or even how to find it. A hint is great!

Thanks.

 

[ideasrule]

After one oscillation, what percentage of the initial amplitude will the actual amplitude be? Call this percentage k. After one oscillation, A=kAi. After two, A=k*k*Ai. After 5, A=k*k*k*k*k*Ai. What's the general formula for A in terms of Ai?

 

[kerimek]

As a scientist, the first step in solving this problem would be to understand the basic principles of oscillation and amplitude. An oscillator is a system that has a regular and repeated motion around an equilibrium point. The amplitude of an oscillator is the maximum displacement from the equilibrium point. In this case, the initial amplitude is given as 6.40 cm.

Next, we need to understand the concept of damping. Damping is the gradual decrease in the amplitude of an oscillator over time due to the dissipation of energy. In this problem, the amplitude decreases by 2.50% during each complete oscillation, which means that after each oscillation, the amplitude is 97.50% of the previous amplitude.

To calculate the amplitude after 50 oscillations, we can use the formula A_n = A_0 * (0.975)^n, where A_n is the amplitude after n oscillations, A_0 is the initial amplitude, and n is the number of oscillations. Plugging in the values, we get A_50 = 6.40 * (0.975)^50 = 0.023 cm. Therefore, after 50 oscillations, the amplitude would be 0.023 cm.

I hope this helps in understanding how to approach this problem. It is important to have a clear understanding of the concepts involved before applying any formula.