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How is the period of a pendulum affected when its point of suspension is (a) moved horizontally in the plane of oscillation with acceleration a; (b) moved vertically upward with acceleration a; (c) moved vertically downward with acceleration a g? Which case, if any, applies to a pendulum mounted on a cart rolling down an inclined plane? How is the period of a pendulum affected when its point of suspension is (a) moved horizontally in the plane of oscillation with acceleration a; (b) moved vertically upward with acceleration a; (c) moved vertically downward with acceleration a g? Which case, if any, applies to a pendulum mounted on a cart rolling down an inclined plane?
The period T of a simple pendulum is defined as,T = 2π√L/gHere L is the length of the pendulum and g is the free fall acceleration.So, the period of the simple pendulum is independent of the mass m of the suspended particle.(a)The period T of the pendulum, when its point of suspension is moved horizontally in the plane of oscillation with acceleration a will be,T = 2π√L/g.The pendulum will oscillate horizontally in the plane. So, it will never change, when its point of suspension is moved horizontally(b)The period T of the pendulum, when its point of suspension is moved vertically upward with acceleration a will be,T = 2π√L/a-g.(c)The period T of the pendulum, when its point of suspension is moved vertically downward with acceleration a < g will be,T = 2π√L/g-aBut when, a > g, the time period of the pendulum will be imaginary. So, there is no oscillation in this case.The period of oscillation, if any, applies to a pendulum mounted on a cart rolling down an inclined plane will be,T = 2π√L/g cosθ-aHere, θ is the angle of inclination
The period T of a simple pendulum is defined as, T = 2π√L/g Here L is the length of the pendulum and g is the free fall acceleration. So, the period of the simple pendulum is...
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