Physics Question?

Question

Does anyone know how to calculate Amplitude when given the velocity function and the mass on a simple harmonic motion with a spring problem?

The velocity equation is: V = (3.60 m/s)sin([(4.71s^-1)t - pi/2])
the springs mass is negligable and there is a .500 kg mass on the end of the spring.

please help. I am so stuck.

Answer 1

From your velocity equation, you know that

ω t = (4.71 1/s ) t

For a mass on a spring, the angular velocity can also be expressed in terms of the mass and spring constant:

ω = sqrt ( k / m )

You know m; now you can find k.

The maximum velocity occurs when the trig function has a value of 1; that's vmax = 3.60 m / s. So now you know that at the instant that the mass crosses the center, all of the energy is kinetic

E = 1/2 m vmax^2

When the spring is stretched to the maximum amount (that is, the amplitude), all of the energy is potential

E = 1/2 k A^2

Set these two energies equal, use the k you found earlier, and solve for the amplitude A.

Answer 2

sdd