The formulas to calculate displacement, velocity, and acceleration in simple harmonic motion are:
\[ y = A \sin(\omega t) \]
\[ v = A \omega \cos(\omega t) \]
\[ a = - A \omega^2 \sin(\omega t) \]
Where:
Simple harmonic motion is defined as the motion of a frictionless pendulum or suspended mass. It describes the oscillatory motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement.
Let's assume the following values:
Using the formulas:
\[ y = 5 \sin(2 \times 3) = 5 \sin(6) = -1.41 \]
\[ v = 5 \times 2 \cos(2 \times 3) = 10 \cos(6) = 9.60 \]
\[ a = - 5 \times 2^2 \sin(2 \times 3) = - 20 \sin(6) = 5.64 \]
The displacement is -1.41, the velocity is 9.60, and the acceleration is 5.59.