An oscillatory pendulum has a velocity of 2m/s at the equilibrium position O and velocity at the same point P calculate the height of P above O (take g=10m/s^2)

Answer 1

To find the height of point P above O, we need to consider the conservation of mechanical energy in an oscillatory pendulum. The total mechanical energy of the pendulum is the sum of its potential energy and kinetic energy:

E = PE + KE

At the equilibrium position O, the velocity is 2 m/s. This means that the KE is not zero at this point, but the potential energy is zero:

E_O = PE_O + KE_O
E_O = 0 + (1/2)mv^2
E_O = (1/2)m(2)^2
E_O = 2m

At point P, we need to find the height h. The velocity at point P is also 2 m/s. We know that at the maximum height of the oscillation, the velocity is zero (KE = 0). So, the total mechanical energy at point P is equal to the potential energy at that position:

E_P = PE_P
E_P = mgh

Since E_O = E_P, we can equate them:

2m = mgh

Simplifying and solving for h:

2 = gh
h = 2/g

Using the value of g = 10 m/s^2, the height of point P above O is:

h = 2/10
h = 0.2 meters