Introduction:
In a simple pendulum, a mass (bob) is attached to a string or rod and allowed to swing back and forth. The motion of the pendulum can be described using the principles of oscillation and conservation of energy. In this case, we are given the angular amplitude and displacement of the pendulum, and we need to determine the tension in the string.

Understanding the problem:
- Angular amplitude: The maximum angle the pendulum swings from its equilibrium position.
- Angular displacement: The current angle of the pendulum from its equilibrium position.

Approach:
We can solve this problem by using the concept of conservation of mechanical energy. At the highest point of the swing, the pendulum is momentarily at rest, and all its energy is in the form of potential energy. At the lowest point of the swing, the pendulum has maximum kinetic energy and minimum potential energy.

Conservation of mechanical energy:
The total mechanical energy (E) of the pendulum is the sum of its potential energy (U) and kinetic energy (K):
E = U + K

Potential energy:
The potential energy of the pendulum is given by the equation:
U = mgh

where m is the mass of the bob, g is the acceleration due to gravity, and h is the height of the bob above its lowest point.

Kinetic energy:
The kinetic energy of the pendulum is given by the equation:
K = (1/2)mv^2

where m is the mass of the bob and v is its velocity.

Equating potential and kinetic energy:
At the highest point of the swing, when the angular displacement is 60 degrees, the bob is momentarily at rest, so its velocity is zero. Therefore, the kinetic energy is zero, and the total mechanical energy is equal to the potential energy.

E = U
(1/2)mv^2 = mgh

Tension in the string:
The tension in the string can be determined using the centripetal force acting on the bob at any point in the swing. The centripetal force is given by the equation:
F = mω^2r

where m is the mass of the bob, ω is the angular velocity, and r is the length of the string.

Angular velocity:
The angular velocity (ω) can be determined using the equation:
ω = v/r

where v is the linear velocity of the bob and r is the length of the string.

Equating centripetal force and tension:
At any point in the swing, the centripetal force acting on the bob is equal to the tension in the string.

F = T = mω^2r

Solving the problem:
We can now solve the problem by substituting the values given and using the equations derived.

1. Calculate potential energy:
U = mgh = m * g * h

2. Calculate kinetic energy:
K = (1/2)mv^2 = (1/2) * m * 0^2 = 0

3. Equate potential and kinetic energy:
E = U
(1/2)mv^2 = mgh
(1/2) * m * 0^2 = m * g * h