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.

There are standard equations for this...I assume you have them. What is troubling you on this?

To find the amplitude and phase angle of the block's motion, we can use the equation for simple harmonic motion (SHM). In SHM, the equation for displacement as a function of time is given by:

x(t) = A cos(ωt + φ)

Where:
- x(t) is the displacement of the block at time t,
- A is the amplitude of the motion,
- ω is the angular frequency of the motion (related to the spring constant and mass),
- φ is the phase angle of the motion.

Let's go through the steps to find the amplitude and phase angle:

Step 1: Find the angular frequency (ω)
The angular frequency is given by ω = √(k/m), where k is the spring constant (340 N/m) and m is the mass of the block (1.65 kg).
ω = √(340 N/m / 1.65 kg)
ω ≈ 11.44 rad/s

Step 2: Find the amplitude (A)
To find the amplitude, we need to find the maximum displacement of the block during its motion. In this case, the block is initially moving in the negative direction at a speed of 12.7 m/s.

Using the equation of motion in SHM, we can equate the initial kinetic energy to the potential energy of the spring:

(1/2)mv^2 = (1/2)kA^2

Where v is the initial velocity of the block and A is the amplitude we want to find.

Substituting the given values:
(1/2)(1.65 kg)(12.7 m/s)^2 = (1/2)(340 N/m)A^2

Simplifying the equation:
107.35 kg·m^2/s^2 = 170 N·A^2

Solving for A:
A^2 = 107.35 kg·m^2/s^2 / 170 N
A^2 ≈ 0.631 kg·m/s^2

Taking the square root, we find:
A ≈ 0.794 m

Hence, the amplitude (A) is approximately 0.794 m.

Step 3: Find the phase angle (φ)
To find the phase angle, we need additional information, such as the displacement or velocity of the block at a specific time.
Without such information, we cannot determine the phase angle in this case.

Therefore, the phase angle (φ) cannot be determined without additional information.