The maximum speed of a 3.2-kg mass attached to a springis 0.65 m/s, and the maxi

Question

The maximum speed of a 3.2-kg mass attached to a springis 0.65 m/s, and the maximum force exerted on the mass is11 N. a) What is the amplitude of motion for this mass? b) What is the force constant of the spring? c) What is the frequency of the system? The maximum speed of a 3.2-kg mass attached to a springis 0.65 m/s, and the maximum force exerted on the mass is11 N. a) What is the amplitude of motion for this mass? b) What is the force constant of the spring? c) What is the frequency of the system?

Explanation / Answer

    Mass, M = 3.2 kg     Vmax = 0.65 m/s     Fmax = 11 N     Fmax = M a max     11 = 3.2 * a max     a max = 3.44 m/s^2 (a)     Vmax = A    ( Vmax ) 2 = 2 A2 .......(1)     a max = 2A            ........(2)     By dividing (1) with (2)     0.65 2 / 3.44 = A     Amplitude, A = 0.123 m (b)     Angular frequency, = Vmax /A                                     = 0.65 / 0.123                                     = 5.28 rad/s     Force constant, K = M 2                                = 3.2 * 5.282                                = 89.4 N/m (c)     Frequency, f = / 2                        = 5.28 / 2                        = 0.841 Hz

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