What is the formula of time period of compound pendulum?

Thus, there are two points of the compound pendulum for the same periodic time at a distance l1 and of the 2 (l2=k2/l1) about the centre of gravity, we get four points on the axis passing through point of suspension and centre of gravity. The time period is same for these four points.

What is the equation for the resulting oscillatory motion?

For a simple harmonic oscillator, an object’s cycle of motion can be described by the equation x ( t ) = A cos ⁡ ( 2 π f t ) x(t) = A\cos(2\pi f t) x(t)=Acos(2πft)x, left parenthesis, t, right parenthesis, equals, A, cosine, left parenthesis, 2, pi, f, t, right parenthesis, where the amplitude is independent of the …

How does the simple pendulum work?

A simple pendulum consists of a mass m hanging from a string of length L and fixed at a pivot point P. When displaced to an initial angle and released, the pendulum will swing back and forth with periodic motion.

How do you derive the equation of motion?

There are three equations of motion that can be used to derive components such as displacement(s), velocity (initial and final), time(t) and acceleration(a)….Definition of Equations of Motion

1. First Equation of Motion : v=u+at. v = u + a t.
2. Second Equation of Motion : s=ut+12at2.
3. Third Equation of Motion : v2=u2+2as.

What is simple pendulum and compound pendulum?

The main difference between simple pendulum and compound pendulum is that, in a simple pendulum, the distance between the centre of gravity of the suspended body and the axis of suspension is large compared to the dimensions of the suspended body whereas, in a compound pendulum, the dimensions of the suspended body are …

What is compound pendulum formula?

The compound pendulum Let G be the centre of gravity of a compound pendulum of mass m that oscillates about a point O with OG = h If the pendulum is moved so that the line OG is displaced through an angle θ (Figure 1), the restoring couple is: – mghsinθ = – mghθ = if θ is small.

What is the equation of simple harmonic motion?

That is, F = −kx, where F is the force, x is the displacement, and k is a constant. This relation is called Hooke’s law. A specific example of a simple harmonic oscillator is the vibration of a mass attached to a vertical spring, the other end of which is fixed in a ceiling.

What is the equation for the period of a simple pendulum?

The equation for the period of a simple pendulum starting at a small angle α (alpha) is: T = 2π√ (L/g) where. T is the period in seconds (s) π is the Greek letter pi and is approximately 3.14. √ is the square root of what is included in the parentheses. L is the length of the rod or wire in meters or feet.

How do you find the angular displacement of a simple pendulum?

By measuring the length and the period of a simple pendulum we can determine g. s = Lθ. The angular displacement of a pendulum is represented by the equation θ = 0.32*cos (ωt) where θ is in radians and ω = 4.43 rad/s. Determine the period and length of the pendulum.

How do you calculate simple pendulum torque?

Time Period of Simple Pendulum Derivation. Using the equation of motion, T – mg cosθ = mv 2L. The torque tending to bring the mass to its equilibrium position, τ = mgL × sinθ = mgsinθ × L = I × α. For small angles of oscillations sin ≈ θ, Therefore, Iα = -mgLθ. α = -(mgLθ)/I.

What is the acceleration due to gravity when a pendulum is moved?

A simple pendulum with a period of 2.00000 s in one location where g = 9.80 m/s 2 is moved to a new location where the period is now 1.99796 s. What is the acceleration due to gravity at its new location? Solution: For a simple pendulum the period T = 2π)/ω is proportional to 1/g 1/2.