Spring-Block system executing SHM in a freely falling elevator

[WannabeNewton]

If $\frac{\mathrm{d} ^{2}x_{\text{eq}}}{\mathrm{d} t^{2}} = g$ then what is $x_{\text{eq}}(t)$ if the initial height of $x_{\text{eq}}$ above the ground was some value $d$ and it started off at rest before going into free fall?

 

[vijaypandey93]

If $\frac{\mathrm{d} ^{2}x_{\text{eq}}}{\mathrm{d} t^{2}} = g$ then what is $x_{\text{eq}}(t)$ if the initial height of $x_{\text{eq}}$ above the ground was some value $d$ and it started off at rest before going into free fall?

Then xequili(t)=g.(t^2)/2 + d

 

[WannabeNewton]

Then xequili(t)=g.(t^2)/2 + d

Right so plugging back into Newton's 2nd law we have $m\ddot{x} = -kx + mg + k(\frac{1}{2}gt^{2} + d)$ in the ground frame. Is this the equation for simple harmonic motion? If you solve this will you get an $x(t)$ that is purely sinusoidal?

 

[vijaypandey93]

Right so plugging back into Newton's 2nd law we have $m\ddot{x} = -kx + mg + k(\frac{1}{2}gt^{2} + d)$ in the ground frame. Is this the equation for simple harmonic motion? If you solve this will you get an $x(t)$ that is purely sinusoidal?

we can't say that necessarily because simple harmonic motion is caused by a force which has a restoring effect and opposite to the displacement.so all the terms may get added and may give a positive value which is ofcourse not the hall mark of SHM.

 

[vijaypandey93]

Right so plugging back into Newton's 2nd law we have $m\ddot{x} = -kx + mg + k(\frac{1}{2}gt^{2} + d)$ in the ground frame. Is this the equation for simple harmonic motion? If you solve this will you get an $x(t)$ that is purely sinusoidal?

okay i'll solve and then check it.thanks a lot

 

[WannabeNewton]

You don't have to explicitly solve it if you don't want to; you can tell just by looking at the equation.