An almost massless spring of spring constant k=188Nmk=188Nm is fixed at one end

Question

An almost massless spring of spring constant k=188Nmk=188Nm is fixed at one end to the top of a frictionless inclined plane as shown above with =28=28 degrees. The other end is attached to a mass m=2kgm=2kg. Take the acceleration of gravity to be 9.81ms29.81ms2.

(a) By what length does the spring stretch when the mass is in equilibrium?

(b) What is the frequency that the mass oscillates, after it has been displaced from its equilibrium.

188 is fied at one end to the top of a fictionless inclined 2kg. Take the acceleration 28 degrees. The other end is attached to a mass m plane as shown above with 0 of gravity to be 9.81 o) By what lengrth does the spring stretch when the massis in equilbrium (b) What is the frequency that the mass oscillates, after it has been displaced from its equilibrium. Hz Submit

Explanation / Answer

a)Forces in vertical direction:

mg sin(theta) = kx

x = mg sin(theta)/k

x = 2 x 9.81 x sin28/188 = 0.044 m

Hence, x = 0.044 m

b)we know that

We know that

f = 1/2 pi sqrt (k/m) = 1/2 x 3.14 sqrt (188/2) = 1.54 Hz

Hence, f = 1.54 Hz

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