Increasing the restoring force in a damped harmonic oscillator has a direct effect on the amplitude of vibration. The restoring force is responsible for pulling the system back toward its equilibrium position when it is displaced. By increasing the restoring force, the system becomes stiffer, making it more difficult for the oscillator to deviate from its equilibrium position.
When the restoring force is increased, the amplitude of vibration for a damped harmonic oscillator decreases. This is because the increased restoring force acts to counteract any displacement from the equilibrium position, leading to smaller oscillations.
In a damped harmonic oscillator, damping refers to the dissipation of energy from the system due to external factors such as friction or air resistance. Damping causes the amplitude of vibration to decrease over time. By increasing the restoring force, the system's ability to resist the dissipative effects of damping is enhanced, resulting in smaller oscillations.
In summary, increasing the restoring force in a damped harmonic oscillator reduces the amplitude of vibration by making the system stiffer and more resistant to displacement from the equilibrium position.