Question

How can a response be compressed in time but have the same peak value?

1) By increasing the frequency of the response
2) By decreasing the frequency of the response
3) By increasing the amplitude of the response
4) By decreasing the amplitude of the response

Answer 1

Increasing the frequency of the response can compress it in time while maintaining the same peak value or amplitude.

Step-by-step explanation:

To compress a response in time while maintaining the same peak value, one can increase the frequency of the response. Increasing frequency means that the waves or cycles occur more rapidly. This can make the response happen over a shorter period of time without changing the amplitude, which corresponds to the peak value of the response.

Decreasing the frequency would extend the response over a longer period, not compress it, and altering the amplitude would change the peak value rather than the time duration. It's noteworthy that, while not mentioned in the original options, resonance is a phenomenon where a small driving force at a resonant frequency can create a large-amplitude response without affecting the time duration significantly.