A 4.0kg mass is attached to a spring that has a springconstant, k=2500N/m, and i

Question

A 4.0kg mass is attached to a spring that has a springconstant, k=2500N/m, and is resting on a frictionless horizontalsurface. The spring is stretched by pulling on the mass until theamount of potential energy in the spring is 4.5J. The block is thenreleased and oscillates in simple harmonic motion. A. What is the amplitude of the oscilltion? B. What is the maximum velocity of the block? C. How long does it take for the block to go from maximumspring length to minimum spring length? D. What is the velocity of the mass when it is 1.5cm from thespring's equilibrium point? A 4.0kg mass is attached to a spring that has a springconstant, k=2500N/m, and is resting on a frictionless horizontalsurface. The spring is stretched by pulling on the mass until theamount of potential energy in the spring is 4.5J. The block is thenreleased and oscillates in simple harmonic motion. A. What is the amplitude of the oscilltion? B. What is the maximum velocity of the block? C. How long does it take for the block to go from maximumspring length to minimum spring length? D. What is the velocity of the mass when it is 1.5cm from thespring's equilibrium point?

Explanation / Answer

mass m = 4 kg spring constant k = 2500 N / m potential energy P = 4.5 J (A). we know P = ( 1/ 2) k A^ 2 from this amplitude A = [2P / k ]                                   =0.06 m = 6 cm (B). Maximum velocity V = A w                                       = A [ k / m]                                      = 1.5 m / s             

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