A cart M is attached to the vertical spring of force constant K so that the spring stretch is 50cm. When the cart is set to oscillatory motion of the vertical spring the period is 10s. If the cart is set on an incline angled 37 degrees and is attached to the top of the plane by the same spring, what is the period of the oscillatory motion that the cart undergoes for this incline?

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A cart M is attached to a vertical spring of force constant K so that the spring stretches 50cm. When the cart is set to oscillatory motion of the vertical spring. The period is 10s.

If the time period of motion for a mass M suspended from a spring with...

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A cart M is attached to a vertical spring of force constant K so that the spring stretches 50cm. When the cart is set to oscillatory motion of the vertical spring. The period is 10s.

If the time period of motion for a mass M suspended from a spring with spring constant K is T, the frequency is `f = 1/T` , angular frequency is `(2*pi)/T = sqrt(K/M)` .

The information provided in the problem gives `sqrt(K/M) = (2*pi)/10` .

The cart is then set on an inclined plane sloping upwards at 37 degrees to the horizontal and suspended from the same spring. If it is assumed that the surface of the inclined plane is frictionless, the time period of oscillatory motion does not change. It remains the same at 10 s. The amplitude of oscillation is decreased in the case where the spring in on the inclined plane compared to being suspended horizontally.

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