Question

An object moves with simple harmonic motion. If the amplitude and the period are both doubled, the object's maximum speed is 1. quartered 2. halved 3. quadrupled. 4. doubled 5. unchanged

Answer 1

If the amplitude and period of an object's simple harmonic motion are both doubled, the object's maximum speed will be halved.

Step-by-step explanation:

When an object moves with simple harmonic motion, doubling the amplitude and period will affect various properties of the motion. In this case, if the amplitude and the period are both doubled, the object's maximum speed will be halved. This means that the object will reach its maximum velocity at a slower rate compared to its original motion.

To understand why this happens, it's important to know that in simple harmonic motion, the maximum speed occurs when the object passes through equilibrium. Doubling the period means that the object will take twice as long to complete one full cycle, which results in a decrease in its maximum speed by a factor of 2.

Answer 2

The object's maximum speed remains unchanged.

Step-by-step explanation:

The speed of a particle in SHM is given by :

`v(t)=A\omega\ sin(\omega t)`

Maximum speed is,
`v_(max)=A\omega`

If A' = 2A and T' = 2T

`v'_(max)=(2A)(2\pi)/(2T)`

`v'_(max)=(A)(2\pi)/(T)`

`v'_(max)=v_(max)`

So, the maximum speed of the object remains the same i.e. it remains unchanged. Hence, this is the required solution.