A `1kg` block is executing simple harmonic motion of amplitude `0.1m` on a smooth horizontal surface under the restoring force of a spring of spring constant `100 N//m`. A block of mass `3 kg` is gently placed on it at the instant it passes through the mean position. Assuming that the two blocks move together. Find the frequency and the amplitude of the motion.

Explanation

To solve the problem step by step, we will calculate the frequency and amplitude of the motion after a 3 kg block is placed on a 1 kg block executing simple harmonic motion.

### Step 1: Calculate the initial frequency of the 1 kg block

The formula for the frequency \( f \) of a mass-spring system is given by:

\[
f = \frac{1}{2\pi} \sqrt{\frac{k}{m}}
...