I have attached image containing the questions

a.what is the period of the oscillation of the block and b. What is the velocity of the block when it first comes back to the equilibrium position

To tackle the questions regarding the oscillation of a block, we need to consider the principles of simple harmonic motion (SHM). Let's break down each part of your inquiry step by step.

Understanding the Period of Oscillation

The period of oscillation refers to the time it takes for the block to complete one full cycle of motion. In the context of SHM, the period (T) can be calculated using the formula:

• T = 2π√(m/k)

Here, m represents the mass of the block, and k is the spring constant. If you have these values from the image you mentioned, you can plug them into the formula to find the period. For example, if the mass is 2 kg and the spring constant is 50 N/m, the calculation would look like this:

• T = 2π√(2/50) ≈ 0.79 seconds

Velocity at the Equilibrium Position

Next, let’s determine the velocity of the block when it first returns to the equilibrium position. In SHM, the velocity is maximum at the equilibrium point. The formula for maximum velocity (v_max) is given by:

• v_max = Aω

In this equation, A is the amplitude of the oscillation, and ω (angular frequency) can be calculated using:

• ω = 2π/T

Substituting the period you calculated earlier into this formula will give you ω. For instance, if T is 0.79 seconds, then:

• ω = 2π/0.79 ≈ 7.93 rad/s

Now, if the amplitude (A) is, say, 0.1 m, you can find the maximum velocity:

• v_max = 0.1 m * 7.93 rad/s ≈ 0.793 m/s

Putting It All Together

In summary, to find the period of oscillation, use the mass and spring constant in the period formula. For the velocity at the equilibrium position, calculate the angular frequency from the period, then apply it to the amplitude to find the maximum velocity. If you provide the specific values from your image, I can help you with the exact calculations!