A box of mass M is attached to a spring and oscillates parallelly to a perfectly smooth inclined plane of angle Z. The spring has constant K. Find the period of oscillation if M=1 Kg, K=1 N/m and Z=30°. Your answer in X.XX s.
Question
A box of mass M is attached to a spring and oscillates parallelly to a perfectly smooth inclined plane of angle Z. The spring has constant K. Find the period of oscillation if M=1 Kg, K=1 N/m and Z=30°. Your answer in X.XX s.
Solution
The period of oscillation of a mass-spring system is given by the formula T = 2π√(m/k), where m is the mass, k is the spring constant, and T is the period. However, in this case, the system is on an inclined plane, so the effective mass is m*cos(Z), where Z is the angle of inclination.
Given that m = 1 kg, k = 1 N/m, and Z = 30°, we can substitute these values into the formula:
T = 2π√((m*cos(Z))/k)
First, calculate the cosine of 30 degrees, which is √3/2.
So, the effective mass m*cos(Z) = 1 kg * √3/2 = √3/2 kg.
Substitute this value and the given value of k into the formula:
T = 2π√((√3/2 kg)/(1 N/m)) = 2π√(√3/2 s²) = 2π*(√3/√2) s = π√6 s.
So, the period of oscillation is approximately 7.64 s.
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