Question

A mass vibrates on an ideal spring as illustrated. The total energy of the spring is 100j. What is the kinetic energy of the mass of point p, halfway between the equilibrium point and the amplitude?

Answer 1

Using energy conservation we know that total energy at point P will be 100 J

Total energy = kinetic energy + potential energy

TE = KE + PE

At max amplitude point total energy will be:

TE = KE1 + PE1,

At max amplitude velocity of mass is zero, So KE = 0 at that point

PE1 = (1/2)*k*A^2 = 100 J

Now at point P

TE = KE2 + PE2

PE2 = (1/2)*k*x^2, since at point P, x = A/2, So

PE2 = (1/2)*k*(A/2)^2 = (1/4)*(1/2)*k*A^2

PE2 = (1/4)*PE1 = (1/4)*100

PE2 = 25 J

And we know that TE = 100 J

So, KE2 = Kinetic energy at point P = TE - PE2

KE2 = 100 - 25 = 75 J