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December 22, 2014

December 22, 2014

Posted by **Anonymous** on Saturday, December 4, 2010 at 9:48pm.

A 52 g mass is attached to a massless spring and allowed to oscillate around an equilibrium according to:

y(t) = 0.8 * sin( 3.8 * t ) where y is measured in meters and t in seconds.

(a) What is the spring constant in N/m?

k = .750880 N/m

(b) What is the Total Energy in the mass and spring in J?

E = ???J

HELP: The total energy is the sum of the kinetic energy and potential energy. At what point in the motion is the energy all kinetic? At what point is it all potential? Can you compute it at this point?

HELP: Kinetic energy is 1/2 * Mass * v2

Potential energy is 1/2 * k * y2

We know that at the mass's maximum y-position it has zero velocity, so simply compute Potential Energy at that point.

- Physics -
**Marco**, Saturday, December 4, 2010 at 11:01pmAt equilibrium position, K.E.=max,P.E. = 0

At the two extreme points, K.E.=0,P.E.=max

Total energy is constant at ANY POINT.

We find E at extreme point.

E = 1/2*k*(0.8)^2

= 0.24J

- Physics -
**Damon**, Saturday, December 4, 2010 at 11:02pmbut you know the velocity

dy/dt = .8 * 3.8 cos (3.8 t)

maximum velocity when sin (3.8 t) = 1

si

max Ke = total = (1/2) (.052)(.8*3.8)^2

- Physics -
**Marco**, Saturday, December 4, 2010 at 11:10pmlol, both method can find the answer

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