Simple Harmonic Motion of a spring and hammer

AI Thread Summary
To determine the amplitude of a mass-spring system after being struck by a hammer, the maximum excursion from equilibrium can be calculated using energy conservation principles. The kinetic energy imparted to the mass at t = 0 is converted into potential energy stored in the spring at maximum displacement. The equation used is (1/2)mv_0^2 = (1/2)kA^2, where m is the mass, v_0 is the initial speed, k is the spring constant, and A is the amplitude. The user confirmed that applying this equation successfully yielded the correct amplitude. Understanding the relationship between kinetic and potential energy is crucial for solving such problems.
SnowOwl18
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What seems to be a very simple question is confusing me.

----At t = 0, a 790g mass at rest on the end of a horizontal spring (k = 101N/m) is struck by a hammer, which gives it an initial speed of 2.66m/s. Determine the amplitude.-----

I know that the amplitude is the 'maximum excursion from equilibrium'. I'm not sure how I can calculate that with the given information. In previous problems I calculated the period to be 0.556s and the frequency to be 1.80 Hz. I'm not sure if I need those two values to find it. Could anyone help me out? Thanks :)
 
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SnowOwl18 said:
What seems to be a very simple question is confusing me.

----At t = 0, a 790g mass at rest on the end of a horizontal spring (k = 101N/m) is struck by a hammer, which gives it an initial speed of 2.66m/s. Determine the amplitude.-----

You haven't provided all the necessary information. I assume that this is a frictionless surface that the mass is sitting on.

The amplitude is the maximum extension of the spring. This occurs when all of the kinetic energy of the mass is used up and stored as potential energy of the spring. So:

\frac{1}{2}mv_0^2 = \frac{1}{2}kA^2

Solve for A (amplitude).

AM
 
Last edited:
that's all the information that was given in the problem. but i just tried your equation and it worked...thanks so much! it was very helpful :)
 

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