A body moving in simple harmonic motion has maximum acceleration when it has
-minimum potential energy.
-maximum kinetic energy.
-maximum velocity.
-Zero displacement.
-minimum kinetic energy.
To determine when a body moving in simple harmonic motion has maximum acceleration, let's understand the characteristics of simple harmonic motion first.
In simple harmonic motion, the restoring force acting on the body is directly proportional to the displacement but acts in the opposite direction. Mathematically, this is expressed as F=-kx, where F is the restoring force, k is the spring constant, and x is the displacement from the equilibrium position.
According to Newton's second law of motion, F=ma, where m is the mass of the body and a is its acceleration. Substituting F from the equation above, we get ma=-kx.
Rearranging the equation, we find that acceleration(a) is directly proportional to the negative displacement(x), which means that a ∝ -x.
Now, keeping this relationship in mind, let's consider the given options:
1. Minimum potential energy: Potential energy is related to displacement and not to acceleration, so this is not correct.
2. Maximum kinetic energy: Kinetic energy is not directly related to acceleration, so this is not correct.
3. Maximum velocity: Velocity is related to acceleration, but in simple harmonic motion, the maximum velocity occurs when the body passes through the equilibrium position, not when the acceleration is maximum. Hence, this is not correct.
4. Zero displacement: With zero displacement, the body is at the equilibrium position. At this point, the acceleration is zero, so this is not correct.
5. Minimum kinetic energy: The kinetic energy is directly related to the square of the velocity. When the velocity is maximum, the kinetic energy is maximum. As mentioned earlier, maximum velocity occurs when the body passes through the equilibrium position, and at this point, the acceleration is maximum. Therefore, the correct answer is minimum kinetic energy.
In summary, a body moving in simple harmonic motion has maximum acceleration when it has minimum kinetic energy.