1. A vibrating point on a spring travels 60 mm during three cycles. What is the amplitude of the vibration?

my answer: I got 10 mm but I'm not sure if it is the correct answer.

2. For two connect pendulums to resonate, they must have the same:
a) mass
b) amplitude
c) density
d) length
e) temperature
my answer: d-length

3. What will be the result if a crest with an amplitude of 30 cm overlaps a trough with an amplitude of 5.0 cm?
a) crest with an amplitude of 35 cm
b) trough with an amplitude of 35 cm
c) crest with an amplitude of 25 cm
d) trough with an amplitude of 25 cm
e) crest with an amplitude of 6 cm
my answer: c

agree with all of them

1. To find the amplitude of vibration, we need to divide the total distance traveled during three cycles by six (since each cycle consists of one crest and one trough). Therefore, the amplitude is given by:

Amplitude = Total distance traveled / 6
= 60 mm / 6
= 10 mm

So, your answer of 10 mm is correct.

2. For two connected pendulums to resonate, they must have the same length. Therefore, the correct answer is d) length.

3. When a crest overlaps with a trough in a wave, they cancel each other out and their amplitudes are subtracted. In this case, the crest has an amplitude of 30 cm and the trough has an amplitude of 5.0 cm.

Amplitude = |Crest amplitude| - |Trough amplitude|
Amplitude = 30 cm - 5.0 cm
Amplitude = 25 cm

So, the correct answer is c) a crest with an amplitude of 25 cm.

1. To find the amplitude of the vibration, you need to understand what is meant by "three cycles." In the context of a vibrating point on a spring, one cycle refers to the motion from one extreme (peak or trough) to the other extreme and back. The amplitude is half the distance between the peak and trough of the vibration.

To calculate the amplitude, you can divide the total distance traveled during three cycles (60 mm) by six (since three cycles consist of two parts - from peak to trough and back).

Amplitude = Total Distance Traveled / 6
Amplitude = 60 mm / 6
Amplitude = 10 mm

Your answer of 10 mm is correct.

2. For two connected pendulums to resonate, they must have the same "d) length." Resonance occurs when two systems have the same natural frequency. The natural frequency of a pendulum depends primarily on its length. When two pendulums have the same length, they will oscillate at the same frequency, which allows for resonance.

Therefore, your answer of "d) length" is correct.

3. When a crest overlaps a trough, they will add together. To determine the resulting amplitude, you simply add the amplitudes of the crest and trough.

Given the crest has an amplitude of 30 cm and the trough has an amplitude of 5.0 cm, the resulting amplitude would be 35 cm.

So, the correct answer is "a) crest with an amplitude of 35 cm."

Your answer of "c) crest with an amplitude of 25 cm" is incorrect, as the amplitudes do not subtract from each other.