Sorry the text is so small, just wanted to include the graph - here\'s the q: A

Question

Sorry the text is so small, just wanted to include the graph -  here's the q:

A spring, of negligible mass and which obeys Hooke's Law, supports a mass M on an incline which has negligible friction. The figure below shows the system with mass M in its equilibrium position. The spring is attached to a fixed support at P. The spring in its relaxed state is also illustrated. 

a) Mass M has a value of 285 g. Calculate k, the spring constant.

b)The mass oscillates when given a small displacement from its equilibrium position along the incline. Calculate the period of oscillation. 

Explanation / Answer

From the diagram unstretched length of the spring is L0 = 40 cm The length of the spring after it is loaded is L = sqrt(60^2 + 60^2) = 84.85 cm The elongation l = L-L0 = 44.85 cm = 0.4485 m Let k be the spring constant According to Hooke's law F = kl The horizontal force acting on the block is F = mgsin19.29 F = 0.285 kg*9.8m/s^2*sin19.29 F = 0.9226 N kl = 0.9226 N k = 2.057 N/m the period of the oscillation is T = 2(pi)sqrt(m/k) T = 2*3.14*sqrt(0.285/2.057) T = 2.34 sec

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