4. (a) iua simple harmonic motion the magnitude of the force is given as F=-kx where is the force constant and x is the displacement of the mass m (which is making the SHM) from its equilibrium position.

In simple harmonic motion (SHM), the force acting on an object is directly proportional to its displacement from the equilibrium position and acts in the opposite direction. This relationship is mathematically expressed as:<br /><br />\[ F = -kx \]<br /><br />where:<br />- \( F \) is the restoring force,<br />- \( k \) is the force constant or spring constant, which measures the stiffness of the spring or system,<br />- \( x \) is the displacement from the equilibrium position.<br /><br />The negative sign indicates that the force is a restoring force, meaning it acts in the opposite direction of the displacement, trying to bring the object back to its equilibrium position. This is a fundamental characteristic of SHM, leading to oscillatory motion.