AP Physics C Mechanics 7.2: Frequency and Period of SHM

Block A and Block B of masses m and 3 m, respectively, are arranged in a setup consisting of an ideal spring with spring constant k and a horizontal surface. Friction between the surface and the blocks is negligible except in a region of length D, where the coefficient of kinetic friction between Block A and the surface is $\mu$. Block B is attached to a string of length $\ell$ and negligible mass, as shown in Figure 1. Block A is held against the spring, compressing the spring a distance $x_{\mathrm{c}}$.

At time t=0, Block A is located at position $x=x_{0}$ and is released from rest. After the block is released, the following occurs.

- At time $t=t_{1}$, Block A is at $x=x_{1}$ after traveling a distance $x_{\mathrm{c}}$. Block A moves with speed v, and the spring is at its equilibrium position.

- At time $t=t_{2}$, the left side of Block A is at $x=x_{2}$ after passing through a distance D across the region with nonnegligible friction.

- At time $t=t_{3}$, Block A is at $x=x_{3}$ and Block A collides with and sticks to Block B.

Indicate how the new frequency of oscillation $f_{2 \ell}$ of the system on the new string of length $2 \ell$ will compare to the frequency of oscillation $f_{\ell}$ from the original procedure. $f_{2 \ell}>f_{\ell}$$f_{2 \ell}<f_{\ell}$$f_{2 \ell}=f_{\ell}$

Briefly justify your answer.