Initially, all the springs displayed in the figure are unstretched when a man begins pulling the block. The man applies a constant force $F$ to the block. Determine the amplitude and the frequency of the block's motion.

Question

Initially, all the springs displayed in the figure are unstretched when a man begins pulling the block. The man applies a constant force

F

to the block. Determine the amplitude and the frequency of the block's motion.
Initially, all the springs displayed in the figure are unstretched when a man begins pulling the block. The man applies

Initially, all the springs displayed in the figure are unstretched when a man begins pulling the block. The man applies

Quantrex Academy · Accepted Answer

Correct answer: C. Amplitude: (F(k_2 + k_3))/(k_1 k_2 + k_2 k_3 + k_3 k_1) , Frequency: (1)/(2π) (k_1 k_2 + k_2 k_3 + k_3 k_1)/(M(k_2 + k_3))

The springs k_2 and k_3 are connected in series. Their equivalent spring constant is: k_ 23 = (k_2 k_3)/(k_2 + k_3) This combination is connected in parallel with spring k_1 . The total equivalent spring constant of the system is: k_ eq = k_1 + k_ 23 = k_1 + (k_2 k_3)/(k_2 + k_3) = (k_1 k_2 + k_2 k_3 + k_3 k_1)/(k_2 + k_3) When a constant force F is applied to the block, the equilibrium position shifts by a distance x_0 given by: x_0 = F k_ eq Since the block is initially at rest at the unstretched position, it will perform simple harmonic motion about the new equilibrium position. The amplitude A of this motion is equal to the shift in the equilibrium position: A = x_0 = F k_ eq = (F(k_2 + k_3))/(k_1 k_2 + k_2 k_3 + k_3 k_1) The frequency of the oscillation is given by: f = (1)/(2π) k_ eq M = (1)/(2π) (k_1 k_2 + k_2 k_3 + k_3 k_1)/(M(k_2 + k_3))

Initially, all the springs displayed in the figure are unstretched...

Options

Correct answer

Step-by-step solution

More from Simple Harmonic Motion