- #1

Like Tony Stark

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- Homework Statement
- A body of mass ##10 kg## is connected to a spring of constant ##490 \frac{N}{m}## and it lies on an frictionless inclined plane. The angle formed by the plane and the floor is ##30°##. This block is inside a room which accelerates upwards with ##a=5 \frac{m}{s^2}##. Prove that if the mass is moved away from its equilibrium point, it will experience simple harmonic motion

- Relevant Equations
- Newton's equation

If I write Newton's equations, seen inside the room and with non tilted axis we have:

##x) N.sin(\alpha)-Fe.cos(\alpha)=m.a_x##

##y) N.cos(\alpha)+Fe.sin(\alpha)-m.g-f*=m.a_y##

Where ##f*=ma##, ##Fe## is the elastic force.

Then, how can I realize about simple harmonic motion?

I also can think it with tilted axis, which would be

##x) mg.sin(\alpha)+f*sin(\alpha)-Fe=m.a_x##

##y)N-mg.cos(\alpha)-f*cos(\alpha)=0##

But I can't notice the SHM. I mean, I can't relate that with ##m.\ddot x +k.x=0##

##x) N.sin(\alpha)-Fe.cos(\alpha)=m.a_x##

##y) N.cos(\alpha)+Fe.sin(\alpha)-m.g-f*=m.a_y##

Where ##f*=ma##, ##Fe## is the elastic force.

Then, how can I realize about simple harmonic motion?

I also can think it with tilted axis, which would be

##x) mg.sin(\alpha)+f*sin(\alpha)-Fe=m.a_x##

##y)N-mg.cos(\alpha)-f*cos(\alpha)=0##

But I can't notice the SHM. I mean, I can't relate that with ##m.\ddot x +k.x=0##