A 780-g mass is attached to a vertical spring and lowered slowly until the mass

Question

A 780-g mass is attached to a vertical spring and lowered slowly until the mass rests at its equilibrium position 30 cm below the original length of the spring. It is then set into simple harmonic motion of amplitude 5 cm.What is the frequency and period of the oscillation, the maximum velocity of the oscillating mass, where does the maximum velocity occur, what is the maximum acceleration of the oscillating mass, and Where does this maximum acceleration occur?
* Draw a diagram showing how the total energy of the oscillating system changes with time.

Explanation / Answer

k = mg / x = 0.780 . 9.8 / 0.3 = 25.48 N/m T = 2p v m / k T = 2p v 0.78 /25.48 = 1.099 s f = 0.910 Hz b) V(max) = 2pf . A = 2p . 0.910 . 0.05 = 0.285 m/s ( at the centre of the motion.... at zero displacement from the equilibrium position) c) a(max) = 4p^2f^2 . A = 1.63 m/s/s ( the turning points in the motion, when V = 0 ) d) This is a trick. The total energy is constant - so the graph is a straight horizontal

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