A 200 gram block, attached to the end of an ideal spring (horizontal) with force

Question

A 200 gram block, attached to the end of an ideal spring (horizontal) with force constant k = 70 N/m, undergoes simple harmonic motion with a maximum displacement of 5.0 cm from the relaxed position. Ignore any friction or air resistance.

(a) Compute the amplitude of oscillations

(b) Compute the maximum speed of the block

(c) At which position the velocity of the block is the maximum?

(d) Compute the magnitude of the maximum acceleration of the block.

(e) At which position the acceleration of the block is the maximum?

(f) How much time does it take the block to travel from the one farthest position
to the next?

(g) At which position the acceleration is zero?

(h)  At which position the velocity is zero?

(h) What is the frequency of the oscillations?

(i) What is the total mechanical energy of the block?

(j) Write down the explicit formula of displacement as a function of time. Explicit means all constants are replaced by their values, while time is variable.

Explanation / Answer

Amplitude of oscillations A = 5 cm =0.05 m Force constant k = 70 N / m mass m = 200 g = 0.2 kg maximum speed V = A w = A ?[ k / m ] = 0.9354 m / s Velocity is maximim at equilibrium position Maximum accleration a= Aw ^ 2 = A ( k / m) = 17.5 m / s ^ 2    Amplitude of oscillations A = 5 cm =0.05 m Force constant k = 70 N / m mass m = 200 g = 0.2 kg maximum speed V = A w = A ?[ k / m ] = 0.9354 m / s Velocity is maximim at equilibrium position Maximum accleration a= Aw ^ 2 = A ( k / m) = 17.5 m / s ^ 2   

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