Consider a simple pendulum of length 1.1 m with

m = 2.9 kg.
If the amplitude of the oscillation is 0.11 m (as measured along the circular arc along which it moves), what is the total mechanical energy of the oscillator?
____ Joules

When all the mechanical energy is kinetic energy, the energy is

1/2*m*v^2 = 1/2*m*omega^2*r^2

where m is the mass, r is the radius, and omega is the angular velocity; For a pendulum, the angular velocity is given by omega = (g/r)^0.5

To calculate the total mechanical energy of the oscillator, we need to consider both its kinetic energy and potential energy.

1. First, let's calculate the potential energy:
The potential energy of the oscillator is given by the formula:
PE = m * g * h
where m is the mass of the pendulum bob, g is the acceleration due to gravity, and h is the height of the bob from the reference point (the lowest position of the pendulum).

In this case, the height, h, is equal to the amplitude, A, of the oscillation. So we have:
PE = m * g * A

Substitute the given values:
PE = 2.9 kg * 9.8 m/s^2 * 0.11 m
PE = 3.191 Joules (rounded to three decimal places)

2. Next, let's calculate the kinetic energy:
The kinetic energy of the pendulum is given by the formula:
KE = (1/2) * m * v^2
where m is the mass of the pendulum bob and v is the velocity of the bob at any given point of the oscillation.

In this case, let's assume the maximum kinetic energy occurs when the bob is at the equilibrium position (the lowest point). At this position, all the potential energy has been converted into kinetic energy.
Hence, the maximum kinetic energy will be equal to the potential energy. Thus:
KE = 3.191 Joules (the same as the potential energy calculated earlier)

3. Finally, to find the total mechanical energy, we add the potential energy and kinetic energy:
Total Energy = PE + KE
Total Energy = 3.191 J + 3.191 J
Total Energy = 6.382 Joules

Therefore, the total mechanical energy of the oscillator is 6.382 Joules.