How Is Maximum Velocity Calculated for a Mass on a Spring?

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To calculate the maximum velocity of a mass on a spring, first determine the spring constant (K) using the formula T = 2π√(m/k), where T is the period and m is the mass. For a 1 kg mass with a period of 2.25 seconds, K can be calculated. The maximum velocity in simple harmonic motion can be derived from the displacement equation x = A sin(ω₀t + φ), where A is the amplitude. The maximum velocity occurs at the equilibrium position and can be found by taking the first derivative of the displacement equation. This approach effectively utilizes the principles of simple harmonic motion to find the solution.
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Homework Statement



1Kg mass connected to a horizontal spring with a period of 2.25s .
Find maximum velocity , if amplitude is 6.00cm ?

Homework Equations


Find K using T= 2pi squroot(m/k)


The Attempt at a Solution


Find a from
F=xK = ma
is the Velocity = a/t(period)?
 
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This is a case of simple harmonic motion. We can find the displacement of the mass by using the equation x = Asin(\omega_0t + \phi). You'll want to find the double derivative of this equation to find the maximum velocity of the mass.
 
The velocity is given by the first derivative as usual.
 

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