I don\'t know how to do the last two Example 12.3 Oscillations on a Horizontal S

Question

I don't know how to do the last two

Example 12.3 Oscillations on a Horizontal Surface A 0.600-kg cart connected to a light spring for which the force constant is 19.0 N/m oscillates on a frictionless, horizontal air track (A) Calculate the maximum speed of the cart if the amplitude of the motion is 3.00 cm max (B) What is the velocity of the cart when the position is 2.00 cm? (C) Compute the kinetic and potential energies of the system when the position is 2.00 cm SOLVE IT (A) Calculate the maximum speed of the cart if the amplitude of the motion is 3.00 cm Conceptualize The system oscillates in exactly the same way as the block in the figure Categorize The cart is modeled as a particle in simple harmonic motion -A Several instants in the simple harmonic motion for a block-spring system.

Explanation / Answer

a. if A is the new amplitude,

1/2 x k x A^2 = 1/2 x m x v^2

so, 1/2 x 19 x A^2= 1/2 x 0.6 x 0.225^2

so, A= 3.99 cm

b. 1/2 x m x v^2 = 1/2 x k x (A^2-x^2)= 1/2 x 19 x (0.0399^2-0.027^2) = 1/2 x 19 x (0.00159-0.000729)

so, v= 0.165 m/s

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