- #1

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Is there any way how to analytically solve the differential equation for harmonic oscillations ?

x'' + (kx)/m=0

where m is the mass and k is the spring constant

thanks

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- Thread starter PeetPb
- Start date

- #1

- 29

- 0

Is there any way how to analytically solve the differential equation for harmonic oscillations ?

x'' + (kx)/m=0

where m is the mass and k is the spring constant

thanks

- #2

- 30

- 1

I would substitute x(t)=A*e^(rt) into the ode factor out x(t) and solve for r.

- #3

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- 0

- #4

- 30

- 1

i is just another constant. So you can rewrite i*A = constant. It's no different from multiplying an arbitrary constant by 2. For example, let's say i*A=-2...then to make that happen A=-2/i. The presence of the i doesn't prevent i*A from equalling an arbitrary constant. I hope I didn't make that sound more complicated than it actually is.

- #5

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