A simple pendulum is made from a bob of mass 0.04 kg suspended on a light string of length 1.4 m. Keeping the string taut, the pendulum is pulled to one tntil it has gained a heit of 0.1 m.calculate the total energy of the oscillation?

To calculate the total energy of the oscillation of a simple pendulum, we need to consider both the potential energy and the kinetic energy.

1. Potential Energy: The potential energy at the highest point of the swing is equal to the gravitational potential energy, given by the formula: Potential Energy = mass x gravity x height, where mass is the mass of the bob (0.04 kg), gravity is the acceleration due to gravity (9.8 m/s²), and height is the height gained (0.1 m).

Potential Energy = 0.04 kg x 9.8 m/s² x 0.1 m = 0.0392 Joules

2. Kinetic Energy: At the bottommost point of its swing, all the potential energy is converted into kinetic energy. The kinetic energy is given by the formula: Kinetic Energy = (1/2) x mass x velocity².

To calculate the velocity, we need to use the conservation of mechanical energy. At the highest point, all the mechanical energy is in the form of potential energy, and at the lowest point, all the energy is in the form of kinetic energy.
Potential Energy = Kinetic Energy

0.0392 Joules = (1/2) x 0.04 kg x velocity²

Solving for velocity:
velocity² = (2 x 0.0392 Joules) / (0.04 kg) = 3.92 m²/s²
velocity ≈ √3.92 m²/s² ≈ 1.98 m/s

Now, we can calculate the kinetic energy at the bottommost point:
Kinetic Energy = (1/2) x mass x velocity²
Kinetic Energy = (1/2) x 0.04 kg x (1.98 m/s)² = 0.0784 Joules

3. Total Energy: The total energy of the oscillation is the sum of the potential and kinetic energies.
Total Energy = Potential Energy + Kinetic Energy
Total Energy = 0.0392 Joules + 0.0784 Joules = 0.1176 Joules

Therefore, the total energy of the oscillation of the simple pendulum is approximately 0.1176 Joules.