Can anyone solve this integral for spring mass oscillation?

AI Thread Summary
The discussion revolves around solving an integral related to spring mass oscillation. The original poster expresses difficulty in directly integrating a non-linear equation and mentions an attempt to convert it into a second-order differential equation, which they believe is not allowed. Participants suggest separating variables in the equation to facilitate integration. A standard integral involving a square root is highlighted, with recommendations for using trigonometric substitution or an integral table for assistance. The conversation emphasizes the importance of proper integration techniques in solving the problem.
jin94
Messages
4
Reaction score
0

Homework Statement



Capture.PNG


So this is the question I need to solve. I was told to directly integrate the bottom equation to solve for x(t). I can solve (1) by differentiating (1) to turn it into 2nd order difffeq (mx''=kx), but I think I'm not allowed to do that ... I have no idea how to solve (2) using direct integration. It looks like a difficult non-linear equation to solve to me. please help me T T

Homework Equations

The Attempt at a Solution


I solved (1) by turning into mx''=kx, but I'm not allowed to do that.
 
Physics news on Phys.org
Welcome to PF!

Equation (2) is in terms of the two variables x and t. The ideas is to "separate" the two variables so that just the x variable occurs on one side and the t variable on the other, in such a way that the equation "begs" you to integrate both sides.
 
  • Like
Likes jin94
TSny said:
Welcome to PF!

Equation (2) is in terms of the two variables x and t. The ideas is to "separate" the two variables so that just the x variable occurs on one side and the t variable on the other, in such a way that the equation "begs" you to integrate both sides.

Thank you! but then how do I integrate 1/(a-b*x^2)^(1/2) dx?
 

Thread 'Errors and significant figures'

I multiplied the values first without the error limit. Got 19.38. rounded it off to 2 significant figures since the given data has 2 significant figures. So = 19. For error I used the above formula. It comes out about 1.48. Now my question is. Should I write the answer as 19±1.5 (rounding 1.48 to 2 significant figures) OR should I write it as 19±1. So in short, should the error have same number of significant figures as the mean value or should it have the same number of decimal places as...
View full post »
Thread 'A cylinder connected to a hanging mass'

Thread 'A cylinder connected to a hanging mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

How to solve a differential equation for a mass-spring oscillator?
Replies
2
Views
2K
Spring with mass hangs from the ceiling
Replies
22
Views
1K
Two spring-coupled masses in an electric field (one of the masses is charged)
Replies
1
Views
853
Free Body Diagram of Mass-Spring System
Replies
5
Views
1K
Harmonic Oscillator with Friction
Replies
12
Views
2K
Body attached to a block by a spring, shaped like an inclined plane
Replies
1
Views
891
Estimating damped harmonic oscillator parameters from this plot of the oscillations
Replies
9
Views
2K
Period of Oscillation for mass on a spring.
Replies
2
Views
2K
Getting the equations of motion for this SHM problem
Replies
8
Views
2K
Oscillating horizontal mass attached to a spring with Friction
Replies
1
Views
2K

Hot Threads

Recent Insights

Back
Top