physics question help please circular motion
Hi, I was trying a question but I got stuck on this.
It says show that the shadow on the screen performs shm using the equation SQ (a distance) = rsinwt. The ms says that this is the solution to a=-w^2x but I don't see how?
Thanks!
It says show that the shadow on the screen performs shm using the equation SQ (a distance) = rsinwt. The ms says that this is the solution to a=-w^2x but I don't see how?
Thanks!
Original post by anonymous56754
Hi, I was trying a question but I got stuck on this.
It says show that the shadow on the screen performs shm using the equation SQ (a distance) = rsinwt. The ms says that this is the solution to a=-w^2x but I don't see how?
Thanks!
It says show that the shadow on the screen performs shm using the equation SQ (a distance) = rsinwt. The ms says that this is the solution to a=-w^2x but I don't see how?
Thanks!
Not sure exactly what the question / ms is but a sinusoid is the, almost trivial, solution to
d^2x/dt^2 + w^2 x = 0
either by verification (sub ans in and check), reverse chain rule twice spot, solve 2nd order shm/resonance ode, ... I ssupect they want you to start with the sinusoid, differentiate twice and note that the second derivative is -w^2x, so shm.
(edited 1 month ago)
Original post by mqb2766
Not sure exactly what the question / ms is but a sinusoid is the, almost trivial, solution to
d^2x/dt^2 + w^2 x = 0
either by verification (sub ans in and check), reverse chain rule twice spot, solve 2nd order shm/resonance ode, ... I ssupect they want you to start with the sinusoid, differentiate twice and note that the second derivative is -w^2x, so shm.
d^2x/dt^2 + w^2 x = 0
either by verification (sub ans in and check), reverse chain rule twice spot, solve 2nd order shm/resonance ode, ... I ssupect they want you to start with the sinusoid, differentiate twice and note that the second derivative is -w^2x, so shm.
oh, so differentiating rsinwt twice to find acceleration which would be - -w^2sinwt and did they jsut replace sinwt with x?
Original post by anonymous56754
oh, so differentiating rsinwt twice to find acceleration which would be - -w^2sinwt and did they jsut replace sinwt with x?
Yes. Thats why you get (first order, ordinary differential) equations like radio active decay
dx/dt = -kx
and the solution is x(t) = Ae^(-kt). Note you may need an amplitude on your sin(wt) but it doesnt alter anything, also the double --.
(edited 1 month ago)
Original post by mqb2766
Yes. Thats why you get (first order, ordinary differential) equations like radio active decay
dx/dt = -kx
and the (x(t)) solution is x(t) = e^(-kt). Note you may need an amplitude on your sin(wt) but it doesnt alter anything.
dx/dt = -kx
and the (x(t)) solution is x(t) = e^(-kt). Note you may need an amplitude on your sin(wt) but it doesnt alter anything.
thank you!
Original post by anonymous56754
Hi, I was trying a question but I got stuck on this.
It says show that the shadow on the screen performs shm using the equation SQ (a distance) = rsinwt. The ms says that this is the solution to a=-w^2x but I don't see how?
Thanks!
It says show that the shadow on the screen performs shm using the equation SQ (a distance) = rsinwt. The ms says that this is the solution to a=-w^2x but I don't see how?
Thanks!
Depending on the setup of the circular motion and the projection of the object to produce the shadow.
From the animated GIF (above), we can see that we use the sine function for projection onto the x-axis, while the cosine function is used for projection onto the y-axis.
If the animation is too fast, you can try this Geogebra.
To show that the shadow is performing shm, I would not recommend that you do the following.
Original post by anonymous56754
oh, so differentiating rsinwt twice to find acceleration which would be - -w^2sinwt and did they just replace sinwt with x?
Check with your teacher, if this is allowed in the examination board.
You are supposed to do physics NOT maths in A level Physics exam.
You have not really linked the circular motion to the shm by doing the differentiation.
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