Question

A glider on a horizontal frictionless track is attached to an ideal massless spring that is fixed to a wall. At a point in the glider's simple harmonic motion, 0.750m from the equilibrium position of the system, the glider is moving to the right at 3.00m/s, is accelerating to the left at 1.00m/s² , and has 18.0J of kinetic energy. Find the glider's maximum velocity.

Answer 1

acceleration a = -1 m/s^2

position x = 0.75 m

speed v = 3 m/s

In SHm speed at any position x

acceleration a = -w^2*x                speed v = w*sqrt(A^2-x^2)

-1 = -w^2*0.75

w = 1.155 rad/s

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v = w*sqrt(A^2-x^2)

3 = 1.155*sqrt(A^2-0.75^2)

A = 2.7 m

speed is maximm when x = 0

Vmax = A*w

Vmax = 2.7*1.155 = 3.12 m/s         <<===========answer