frictionless block of mass 1.65 kg is attached to an ideal spring with force constant 340 N/m . At t=0 the spring is neither stretched nor compressed and the block is moving in the negative direction at a speed of 12.7 m/s .

A-Find the amplitude.
B-Find the phase angle.

To find the amplitude and phase angle of the block's motion, we need to use the equation for simple harmonic motion (SHM). The equation for SHM is:

x(t) = A * cos(ωt + φ)

where:
- x(t) is the displacement of the block from its equilibrium position at time t.
- A is the amplitude of motion.
- ω is the angular frequency of motion.
- φ is the phase angle.

Let's calculate these values step by step:

Step 1: Find the angular frequency (ω):
The angular frequency is related to the force constant (k) and the mass (m) of the block in the following way:

ω = sqrt(k/m)

Given:
- Force constant (k) = 340 N/m
- Mass (m) = 1.65 kg

Substituting these values into the equation, we get:

ω = sqrt(340 N/m / 1.65 kg)

Step 2: Find the amplitude (A):
The amplitude of motion is related to the initial conditions of the block's motion. In this case, the block is moving with an initial speed of 12.7 m/s in the negative direction. The amplitude can be calculated using the formula:

A = v₀ / ω

Given:
- Initial speed (v₀) = 12.7 m/s

Substituting the values of v₀ and ω into the formula, we get:

A = 12.7 m/s / ω

Step 3: Find the phase angle (φ):
The phase angle can be calculated using the formula:

φ = arccos(x₀ / A)

In this case, the block is neither stretched nor compressed at t = 0. Therefore, the displacement (x₀) is 0.

Substituting the values of x₀ and A into the formula, we get:

φ = arccos(0 / A)

Now, let's calculate the values:

Step 1:
ω = sqrt(340 N/m / 1.65 kg)

Step 2:
A = 12.7 m/s / ω

Step 3:
φ = arccos(0 / A)

By calculating these equations, you can find the values of the amplitude (A) and phase angle (φ) for the given scenario.