How to Find Constants in a Ball's Simple Harmonic Motion on an Asteroid

[MrRandom66]

Homework Statement

I'm total newbie when it comes to differenciatiation, and was wondering if I'm doing this correct.

Basically, this is a physics problem, but thought I'd put this in the calculus section for specific help.

It's about a ball undergoing SHM, after being dropped down a shaft on an asteroid! (an everyday occurrence you'll find)

I've got to find the constants for A, B, and C.

We haven't been told what they represent, but I'm pretty sure B is velocity, C, acceleration due to gravity (Not Earths gravity, remember) and I think A is either Amplitude, or initial position. I'm not sure.

Homework Equations

x(t) = A + Bt + Ct^2

Where the ball is released at x=R at t=0s

The Attempt at a Solution

Not sure I'm doing this correctly, but for the first derrivative...

R(0s) = A + B x 0s + C 0s^2 = A.

So does this mean, that time at 0s is in position A?

 

[dacruick]

So does this mean, that time at 0s is in position A?

Yes it does.

 

[dacruick]

more importantly it means that A = R

 

[dacruick]

Hmm I'm having trouble going in an editing my posts, I apologize that there are multiple ones. You also know that the ball is released from rest at time 0 as well. What can you do with that equation to find some more information?

 

[MrRandom66]

more importantly it means that A = R

So, I presume A is Initial position, and not the amplitude?

Anyway, second derivative. Velocity.

R(t) = Bt + 2Ct^1

Which is 0 again isn't it? As time = 0s.

Not sure I've done this correctly.

 

[MrRandom66]

Just realized the question does say "at small times the ball has the x-component of the ball has the following form", so shall I change t to perhaps 0.1s to discover position etc?

 

[dacruick]

Not sure I've done this correctly.

You didn't. that 't' in 'Bt' should not be there.

 

[dacruick]

I must go for the day MrRandom. You will find the method of solving these types of equations by googling "Linear Second Order Differential Equations with Constant Coefficients". Good luck to you.

 

[MrRandom66]

Ok thanks for your help. If someone else could help me I'd appreciate it.

 

[MrRandom66]

I think I've got the differenciation part susses.

v(t) = dx/dt = B + 2ct
a(t) = d2x/dt2 = 2c

Now i', supposed to find numerical values for these, but not sure where to begin.