A spring, of negligible mass and which obeys Hooke\'s Law, supports a mass M on

Question

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.

1-Mass M has a value of 235 g. Calculate k, the spring constant.

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


Please include the calculations.

Explanation / Answer

angle with horizontalÂ

tan(theta) = 60/80 Â = 3/4

sin(theta) = 3/5

stretching of spring = 50-20 = 30 cm

balancing the force

kx= mgsin(theta)

k * 3 x 10^-1 Â = 235 x 10^-3 * 9.81 * 3/5

k = 4.6107 N/m

w = 2pi/ sqrt(k/m)

= 1.4185 s

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