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. Mass M has a value of 295 g. Calculate k, the spring constant. _____ Tries 0/10 The mass oscillates when given a small displacement from its equilibrium position along the incline. Calculate the oscillation frequency. _______ Tries 0/10

Explanation / Answer

From the diagram, the unstretched spring has length 20 cm.
The stretched spring has length (60² + 60²) cm = 84.85 cm.
x = 84.85-20 =64.85 cm
angle of incline: = arctan(60/60) = 45º (from spring geometry)
downslope component of weight Fg = mgsin = 0.295kg * 9.8m/s² * sin45º = 2.04 N
spring force = kx = Fg
k * 0.6485m = 2.04 N
k = 3.14 N/m

b) = (k / m) = (3.14kg/s² / 0.295kg) = 3.26 rad/s
f = / 2 =3.26 / 2 = 0.519 Hz

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