- #1

- 100

- 11

Hi community,

I've been looking at solutions for mass spring shm (undamped for now) ie that

x = Acoswt and x = Bcoswt work as solutions for dx

and that the general solution is the sum of these that with a trig identity can be written as

x = C Cos(wt - φ) where C is essentially the amplitude (and is given by √(A

My question is the physical significance of A and B in the two separate solutions above (before this youtube video) I've always gone for the solutions as either the Acoswt or Asinwt (with A being the amplitude) depending on where the mass is in its oscillating cycle at time t=0, i.e. would have gone with the coswt one if

x = +A at t=0.

If I let A and B both be A then my factor C (amplitude) comes out as √(2)A where I want it to represent the Amplitude A.

Would really appreciate help.

regards,

Glenn.

I've been looking at solutions for mass spring shm (undamped for now) ie that

x = Acoswt and x = Bcoswt work as solutions for dx

^{2}/dt^{2}= -(k/m)xand that the general solution is the sum of these that with a trig identity can be written as

x = C Cos(wt - φ) where C is essentially the amplitude (and is given by √(A

^{2}+ B^{2})My question is the physical significance of A and B in the two separate solutions above (before this youtube video) I've always gone for the solutions as either the Acoswt or Asinwt (with A being the amplitude) depending on where the mass is in its oscillating cycle at time t=0, i.e. would have gone with the coswt one if

x = +A at t=0.

If I let A and B both be A then my factor C (amplitude) comes out as √(2)A where I want it to represent the Amplitude A.

Would really appreciate help.

regards,

Glenn.

Last edited by a moderator: