Solving SHM Kinematics: Find the Period!

[G01]

Hi there I'm having a little trouble doing problems with SHM kinematics. I think its because I have yet to find a good method of solving them. I'll post one and show what I can do. Them I hope somone can help me find a good method to solving it.A 1 kg block oscillates on a spring with k= 20 N/m. At t= 0s the block is 20cm to the right of equilibrium. and moving to the left with v= -100cm/s.
What is the Period?All I can figure out is that $$\phi_0 = \cos^{-1} (\frac{x_0}{A})$$

And that $$T= 2\pi \sqrt{\frac{m}{k}} = 1.40s$$

Any hints at all? I can't seem to find any expression for the other variables that'll help, but maybe I'm forgetting some. Any help?

 

[G01]

WAIIIIIIIIIT A MINUTE I SOLVED THIS I forgot what i was solveing for sry!

 

[quicknote]

Hello there,

I understand that you are having trouble with solving SHM kinematics problems and are looking for some guidance. SHM or Simple Harmonic Motion is a fundamental concept in physics and it involves oscillatory motion of a system around an equilibrium point. In your problem, a 1 kg block is oscillating on a spring with a spring constant of 20 N/m.

To find the period of the oscillation, we can use the formula T=2π√(m/k), where m is the mass of the block and k is the spring constant. As you have correctly calculated, the period is 1.40 seconds. However, this formula only works for simple harmonic motion with no initial velocity.

In your problem, the block has an initial velocity of -100 cm/s and is 20 cm to the right of equilibrium at t=0s. To solve this problem, we need to use the equation x(t)=Acos(ωt+φ), where A is the amplitude, ω is the angular frequency and φ is the phase angle. We can find these values by using the initial conditions provided in the problem.

First, we can find the amplitude A by using the formula A=√(x0^2+v0^2/ω^2), where x0 is the initial displacement and v0 is the initial velocity. In this case, A=√(20^2+(-100)^2/ω^2)=√(400+10000/ω^2)=√(10400/ω^2).

Next, we can find the angular frequency ω by using the formula ω=√(k/m), where k is the spring constant and m is the mass of the block. In this case, ω=√(20/1)=√20.

Finally, we can find the phase angle φ by using the formula φ=cos^-1(x0/A), where x0 is the initial displacement and A is the amplitude. In this case, φ=cos^-1(20/√(10400/ω^2)).

Now, we can plug in these values in the equation x(t)=Acos(ωt+φ) to get the equation of motion for the block. From this equation, we can find the period by calculating the time it takes for the block to complete one full oscillation, which is the period.

I hope