The force which does not describe a simple harmonic motion isa)a first order differential equation of degree 2b)a first order linear differential equationc)a second order linear differential equationd)linear in positionCorrect answer is option 'A,B,D'. Can you explain this answer?

Question

Answer

The force that does not describe a simple harmonic motion is the one that satisfies the conditions of being a first order differential equation of degree 2, a first order linear differential equation, and linear in position. Let's break down each condition and understand why it is not applicable to simple harmonic motion.

1. First order differential equation of degree 2:
A first order differential equation of degree 2 implies that the highest derivative of the function involved is squared. In simple harmonic motion, the equation of motion is given by a second order differential equation (not first order) because the acceleration is directly proportional to the displacement and is in the opposite direction. Therefore, simple harmonic motion does not satisfy this condition.

2. First order linear differential equation:
A first order linear differential equation can be written in the form dy/dx + P(x)y = Q(x), where P(x) and Q(x) are functions of x. In simple harmonic motion, the equation of motion is given by a second order differential equation, which is not linear because it contains the square of the dependent variable (displacement). Therefore, simple harmonic motion does not satisfy this condition.

3. Linear in position:
A force is linear in position if it is directly proportional to the displacement. In simple harmonic motion, the force (F) is given by F = -kx, where k is the spring constant and x is the displacement from the equilibrium position. This force is linear in position because it is directly proportional to x. Therefore, simple harmonic motion satisfies this condition.

In summary, the force that does not describe a simple harmonic motion is the one that is a first order differential equation of degree 2, a first order linear differential equation, and not linear in position.

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