Given a cart and spring on incline, how do I find the period of oscillation?

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Turnnirl
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Joined: Mon Oct 15, 2018 7:00 pm

Given a cart and spring on incline, how do I find the period of oscillation?

Post by Turnnirl » Mon Oct 15, 2018 7:00 pm

hi I need a question answered

I need help on b

A cart of mass m is attached to a vertical spring of force constant k so that the spring stretches 20 cm. When the cart is set into oscillatory motion on the vertical spring, the period of the oscillation is 3 seconds. The cart is set on an incline angled at 30 and is attached to the top of the plane by the by the same spring.
(a) What is the stretch of the spring while the cart is on the incline?
(b) What is the period of the oscillatory motion that the cart could undergo on the incline.

For part a I got 10 cm and it was marked correct.

Here's where I'm not sure I'm going in the correct direction. To put in gravity, I introduce an angle theta. But I need to know more to use it.

jeff
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Re: Given a cart and spring on incline, how do I find the period of oscillation?

Post by jeff » Mon Oct 15, 2018 8:06 pm

Hi Turnnirl,
Turnnirl wrote:
Mon Oct 15, 2018 7:00 pm
hi I need a question answered

I need help on b

A cart of mass m is attached to a vertical spring of force constant k so that the spring stretches 20 cm. When the cart is set into oscillatory motion on the vertical spring, the period of the oscillation is 3 seconds. The cart is set on an incline angled at 30 and is attached to the top of the plane by the by the same spring.
(a) What is the stretch of the spring while the cart is on the incline?
(b) What is the period of the oscillatory motion that the cart could undergo on the incline.

For part a I got 10 cm and it was marked correct.

Here's where I'm not sure I'm going in the correct direction. To put in gravity, I introduce an angle theta. But I need to know more to use it.
It turns out that because gravity is a constant force (near earth) and the spring force is a linear force (in displacement) that the force of gravity actually has no effect on the period in these cases. For example, when the spring is horizontal, like on a floor, the mass oscillates about the unstretched spring position. When it is vertical, gravity causes the mass to oscillate about a different point, where the spring is already stretched. But the period of motion about that point is the same.

And on the incline, it's inbetween. Gravity causes the spring's "neutral" position (the "rest" position) to be farther down, but not as far down as the vertical. But still, the period is the same in all 3 cases, because that's just the motion that the spring causes back and forth about the "rest" position.

Does that make sense? The spring will stretch enough to cancel the force of gravity, and then can oscillate about that new point. It can be a tricky point to see how they cancel while the spring length is moving, so please ask if it's not clear.

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