## Mechanical Oscillator vs Electrical Oscillator | difference between Mechanical Oscillator and Electrical Oscillator

This page compares Mechanical Oscillator vs Electrical Oscillator and mentions difference between Mechanical Oscillator and Electrical Oscillator. The equation of electrical oscillator equivalent to harmonic oscillator has also been derived step by step.

**Introduction**: Most of the communication systems
and test and measurement equipments use oscillators for various functions.
Hence specifications and tolerances of these systems and equipments rely on
oscillators used.

There are number of parameters which are considered during the design of
oscillators. They are as follows.

• Frequency sensitivity

• Frequency stability i.e. Short term and long term drifts

• Oscillator noise

• Amplitude stability

### Mechanical Oscillator | Harmonic Oscillator

• The figure-1 depicts simple mechanical oscillator having mass attached to the spring.
This structure is similar to Pendulum. It is also known as harmonic oscillator.

• If a body attached to a spring is displaced from its equilibrium position,
the spring exerts a restoring force on it, which tends to restore the object to the equilibrium position.
This force causes oscillation of the system, or periodic motion.

• f = 1/ T , where "T" and "f" are period of oscillation and
frequency of the oscillation.

• Angular frequency is about 2*π times of frequency i.e. w = 2*π*f

• When the restoring force is directly proportional to the displacement from
equilibrium, the resulting motion is known as simple harmonic motion and
the oscillator is known as Harmonic Oscillator.

### Electrical Oscillator

• The figure-2 depicts electrical analogy of the mechanical oscillator.
This is example of electronic or electrical oscillator. There are different types of oscillators viz.
RC oscillator, LC oscillator, crystal oscillator etc.

• LC circuit is made from an inductor and a capacitor.
Initially capacitor is charged and a current is induced in the inductor.
After this current and voltage oscillate harmonically according to following equation.

• V =Vmax * cos (w*t + Φ), I = Imax * cos (w*t + Φ + 90)

Let us derive differential equation to represent electrical oscillator.

➤Capacitor discharges (or charges) through inductor,
Hence current (I) in inductor and charge (Q) on capacitor are related as

I (t) = dQ/dt.

➤Consequently, voltage on inductor is related to second time derivative of the charge as

V_{L}(t) = - L * dI/dt = - L * d^{2}Q/dt^{2}

➤However in LC circuit, voltage on inductor must be same as voltage on
the capacitor,

Hence V_{L} = V_{C} = Q/C

➤Comparing the last two equations, we can get,

-L * d^{2}Q/dt^{2} = V_{L} = V_{C} = ( 1/C ) * Q(t)

➤This second order differential equation for charge has form of
harmonic oscillator.

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