Whether or not it'll help me, am i safe to deduce that:

If a simple pendulum is released from rest at time t=0;
from a displacement of x rad from equilibrium;

Then the amplitude of the oscilation is also x rad?

Thanks

The answer is "yes". If you gave us the complete question we might have been able to offer more suggestions. If the amplitude is used to get something else, you may want to look at this web page:

http://hyperphysics.phy-astr.gsu.edu/hbase/pendl.html

To determine if the amplitude of the oscillation of a simple pendulum is equal to the initial displacement, you can apply the principles of simple harmonic motion and the properties of a pendulum.

To start, it's important to understand the basic properties of a simple pendulum. A simple pendulum consists of a mass (called the bob) suspended from a fixed point by a massless string or rod. When the bob is displaced from its equilibrium position and released, it oscillates back and forth under the influence of gravity.

In a simple pendulum, the restoring force acting on the bob is directly proportional to the displacement (x) from the equilibrium position and is given by the equation:

F = -m * g * sin(theta)

where m represents the mass of the bob, g is the acceleration due to gravity, and θ is the angular displacement. The negative sign indicates that the force always acts in the opposite direction to the displacement.

When the displacement is small, the motion of the pendulum approximates simple harmonic motion. Simple harmonic motion is characterized by a sinusoidal pattern, such as a sine or cosine wave. In this case, the angular displacement (θ) can be approximated by the equation:

θ = x / L

where L is the length of the pendulum.

Now, the amplitude of the oscillation refers to the maximum angular displacement from the equilibrium position. When a pendulum is released from rest at time t=0, with an initial displacement of x radians, for small angles, the amplitude of the oscillation is indeed approximately equal to x radians. This approximation holds true as long as the angle of displacement remains small, typically less than 15 degrees or around 0.26 radians.

Keep in mind that this explanation assumes no additional factors, such as air resistance or damping, and that the pendulum is simple (without any additional complexities).

In summary, if a simple pendulum is released from rest with an initial displacement of x radians, the amplitude of the oscillation is approximately equal to x radians, as long as the angle of displacement remains small.