- #1
Glenn G
- 113
- 12
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 dx2/dt2 = -(k/m)x
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 √(A2 + B2)
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 dx2/dt2 = -(k/m)x
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 √(A2 + B2)
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.
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