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In Simple Harmonic Motion,

can

(k/m) = ω

be expressed for all SHMs or only the ones in which the mass due to which the SHM is being executed is performing a circular motion?

Since for example, in the case of spring, there is no circular motion involved, so omega should not be defined for spring.

Or if it is a general equation is there a proof to justify?

How I understand this is....

(k/m) = ω

can be derived by comparing

F = -kx ⇒ (d

and

x = Acos(ωt + φ

But is

x = Acos(ωt + φ

a general equation for all SHMs? That is to say, can all SHMs be expressed by this equation or only the ones in which circular motion is involved?

For example,

how would this equation be used for expressing the SHM performed by a spring?

The above equation is using a sinusoidal function and is dealing with angles and there is no angle formed in SHM performed by spring since the SHM is being executed linearly. (The mass because of which SHM is being executed is moving linearly and also performing the SHM)

Or if the equation is a general statement how can we theoretically prove it?

can

(k/m) = ω

^{2}be expressed for all SHMs or only the ones in which the mass due to which the SHM is being executed is performing a circular motion?

Since for example, in the case of spring, there is no circular motion involved, so omega should not be defined for spring.

Or if it is a general equation is there a proof to justify?

How I understand this is....

(k/m) = ω

^{2}can be derived by comparing

F = -kx ⇒ (d

^{2}x/dt^{2}) = (-k/m)and

x = Acos(ωt + φ

_{o}) ⇒ (d^{2}x/dt^{2}) = -ω^{2}xBut is

x = Acos(ωt + φ

_{o})a general equation for all SHMs? That is to say, can all SHMs be expressed by this equation or only the ones in which circular motion is involved?

For example,

how would this equation be used for expressing the SHM performed by a spring?

The above equation is using a sinusoidal function and is dealing with angles and there is no angle formed in SHM performed by spring since the SHM is being executed linearly. (The mass because of which SHM is being executed is moving linearly and also performing the SHM)

Or if the equation is a general statement how can we theoretically prove it?

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