Mass and spring on an inclined plane

[Kenny555]

Homework Statement

[/B]

I got part A and B but in part c , but how to relate period to the equation in part b which is not similar to the cosine function of S.H.M . So i don't know how to obtain period from the equation

PS: In part b ,I use mgsin(theta)=-kx and then divided by m

Homework Equations

:
[/B]
Simple harmonic motion:
-amplitude*(omega)^2 cos(omega(t)+phase angle).

The Attempt at a Solution

[/B]
I directly use (2pi/T)=sqrt(k/m) to find period but i don't how to relate to the equation given in part b

 

[Merlin3189]

Note: you can use the Σ sign on the menu to get access to symbols for omega, pi, etc. Also you can use Latex to set the formulae out neatly.

Q3. This is about the derivation of the formula ##\frac {1} {T} = \frac {1} {2\pi} \sqrt {\frac {k} {m} } ## that you mention.
You can look it up in your notes or on the web.
Essentially, you can show that ## x = A cos(ωt +φ) ## is a solution to the differential equation in part b. Then substituting this solution and equating its second derivative let's you get the T formula from comparing the expressions for the amplitude. (This is all mathematical jiggery pokery, which is why we just remember the resultant formula. It may be worth understanding, because SHM is common in other contexts, which all lead to the same sort of differential eqn.)These are the formulae you quote, written in Latex. If you copy them and put two hash signs in front and at the end, they'll show up properly and you can preview them.

\frac {1} {T} = \frac {1} {2\pi} \sqrt {\frac {k} {m} }

Aω^2cos(ω(t)+θ)

 

[Kenny555]

Thanks a lot!

 

[Max Agarwal]

Can u please tell me the solution of part B.

 

[haruspex]

Can u please tell me the solution of part B.

That's effectively a new question. Please post it as a new thread, filling in the template. In particular, be sure to post an attempt.