What is Driven Simple Harmonic Oscillator?
The driven simple harmonic oscillator is a physics concept explaining the motion of a mass-spring system influenced by an external force.
ANSWER : A driven simple harmonic oscillator refers to a system consisting of a mass attached to a spring that oscillates back and forth under the influence of an external force. The external force, called the driving force, is applied to the system and causes it to vibrate with a specific frequency.Imagine a mass attached to a spring that can move back and forth. When we apply a force to this system, it starts oscillating with a frequency determined by the driving force. This external force can cause the mass to oscillate at a different frequency than its natural frequency, leading to complex motion patterns. Understanding the driven simple harmonic oscillator helps us analyse how systems respond to external forces and design efficient structures and devices.
The equation that represents the Driven Simple Harmonic Oscillator is:
\[m \frac{{d^2x}}{{dt^2}} + b \frac{{dx}}{{dt}} + kx = F_0 \cos(\omega t)\]
In this equation:
- \(m\) represents the mass of the object.
- \(x\) denotes the displacement of the mass from its equilibrium position.
- \(t\) is time.
- \(b\) is the damping coefficient, which determines the strength of the damping force.
- \(k\) is the spring constant, which represents the stiffness of the spring.
- \(F_0\) is the amplitude of the driving force, which determines its strength.
- \(\omega\) is the angular frequency of the driving force, given by \(\omega = 2\pi f\), where \(f\) is the frequency of the driving force.
The equation describes the balance between the inertial force, the damping force, the spring force, and the driving force acting on the mass. The solution to this equation gives the motion of the mass-spring system under the influence of the external force.
Also Read : Define Inertial Frame of Reference.
Also Read : Prove that limiting values of σ is -1 and 0.5.
No comments: