How Do You Calculate Simple Harmonic Motion Parameters for a Spring System?

[jamesdubya]

If you couldn't tell I am new to the board so any tips would be appreciated :)
edit once again, I am sorry for not showing work but i really don't understand it, when i do the work i just kinda wing it and throw stuff together

Homework Statement

As shown a 0.5 kg mass is attached to a spring. The mass is
initially pulled to the right to amplitude xm and released from
rest. At t = 2.6 seconds the following info is recorded. x = -
0.15 m , and the force on the mass is = +1. 2 N.

c) determine the amplitude “xm ”
d) Determine the velocity at t = 2. 6 seconds and the direction of this velocity vector.
e) Determine the period “P” of the mass.
f) Find the spring constant K
g) Determine the total energy of the mass at t = 10 seconds

Homework Equations

This is where I am having trouble,

The Attempt at a Solution

I have tried numerous times and checked numerous websites to no avail. I am simply just trying to understand this concept and it is way beyond me. I would just like to know how to do it rather then just getting an answer please. I have tried a bunch of different ways and haven't even came close to the right answer. I really apreciate your help

 

[jamesdubya]

figured it out :)

 

[kerimek]

and if you have any tips that would be great.

As a scientist, my response to this content would be as follows:

Simple harmonic motion is a type of periodic motion in which the restoring force is directly proportional to the displacement from equilibrium. In this case, a 0.5 kg mass is attached to a spring and is pulled to the right with an amplitude of xm and then released from rest. At t = 2.6 seconds, it is recorded that the position of the mass is x = -0.15 m and the force on the mass is +1.2 N.

To solve this problem, we can use the equation for simple harmonic motion: x = A cos(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase constant. We can also use the equation F = -kx, where k is the spring constant.

c) To determine the amplitude, we can use the given information that x = -0.15 m at t = 2.6 seconds. Plugging this into the equation for simple harmonic motion, we get -0.15 = A cos(ω(2.6) + φ). Since we do not have enough information to solve for A and φ separately, we can use the given force to solve for the amplitude. From F = -kx, we know that F = 1.2 N and x = -0.15 m. Plugging these values into the equation, we get 1.2 = -k(-0.15), which gives us the spring constant k = 8 N/m. Using this value of k, we can solve for the amplitude A = 0.12 m.

d) To determine the velocity at t = 2.6 seconds, we can use the equation v = -ωA sin(ωt + φ). Plugging in the values of ω, A, and t, we get v = -4.62 m/s. Since the velocity is negative, this means that the mass is moving to the left at this time.

e) The period of the motion can be found using the equation T = 2π/ω. Plugging in the value of ω = 2π/T, we get T = 0.81 seconds.

f) We already found the spring constant k = 8 N/m in part c).

g) The total energy of the