Question

A 0.55-kg object connected to a light spring with a force constant of 18.0 N/m oscillates on a frictionless horizontal surface. The spring is compressed 4.0 cm and released from rest.
(a) Determine the maximum speed of the object.
cm/s

(b) Determine the speed of the object when the spring is compressed 1.5 cm.
cm/s

(c) Determine the speed of the object when the spring is stretched 1.5 cm.
cm/s

(d) For what value of x does the speed equal one-half the maximum speed?
cm

Answer 1

you have to use the work energy theorem here
here only one force is doing work on the object that is spring force
so work done by the sprig force = change in the kinetic energy
i'm working on the solution and 'll post it in a few moments

Answer 2

the wrk done by a spring is given by 1/2 kx^2
where k=spring constant and x is the deformation
and you have to equate it with the change in kinetic energy=final k.e.-initial k.e.
and initial kinetic energy=0(released from rest)
so final kinetic energy=1/2 mv^2
where m=mass of the object and v=velocity of the object
so from here by putting the values of m,k,x, you may get the value of the velocity
and this will be the answer to the first question
i'm in a hurry so 'll post the solutions afterwards

Answer 3

@rajat97 I am studying this stuff. I would like to practice. Please correct me if I am wrong. And I need confirmation if I am right, too. Thank you

Answer 4

You are correct, thank you.