Period of a simple harmonic oscillator

In summary, the problem involves a 90.0 kg skydiver on a parachute with a period of 1.50 seconds. When a second skydiver with a mass of 60.0 kg hangs from the legs, the new period of oscillation is 1.94 seconds. The equations used were T = 2 (pi) sqrt(m/k) and y=sinAwt=Asin sqrt(k/m)t, but the calculated period was 0.129 seconds. The student is asking for help with their calculations for the T = 2π... method.
  • #1
spraymonkey32
1
0
Hi I'm having problems with solving this question:
a 90.0 kg skydiver hanging from a parachute bounces up and down with a period of 1.50 seconds. What is the new period of oscillation when a second skydiver, whose mass is 60.0 kg, hangs from the legs first?

the answer is 1.94 seconds


Homework Equations


I think it has something to do with the the simple harmonic oscillator:
T = 2 (pi) sqrt(m/k)
I also tried the simple harmonic equation involving sin:
y=sinAwt=Asin sqrt(k/m)t

but i keep on getting 0.129 seconds.


I attempted this several times and is stuck on how to do it. I am studying for exams and there are several questions similar to it. Can someone help me please! :)
 
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  • #2
Can you show your calculations for the T = 2π... method?
 

FAQ: Period of a simple harmonic oscillator

What is the period of a simple harmonic oscillator?

The period of a simple harmonic oscillator is the time it takes for one complete oscillation or cycle. It is represented by the variable T and is measured in seconds.

What factors affect the period of a simple harmonic oscillator?

The period of a simple harmonic oscillator is affected by the mass of the object, the spring constant of the spring, and the amplitude of the oscillation. The period increases with increasing mass and decreasing spring constant, while it decreases with increasing amplitude.

How is the period of a simple harmonic oscillator calculated?

The period of a simple harmonic oscillator can be calculated using the equation T = 2π√(m/k), where m is the mass of the object and k is the spring constant.

What is the relationship between the frequency and period of a simple harmonic oscillator?

The frequency of a simple harmonic oscillator is the inverse of the period, meaning that as the period increases, the frequency decreases, and vice versa. This relationship is represented by the equation f = 1/T.

What is the significance of the period of a simple harmonic oscillator in real-world applications?

The period of a simple harmonic oscillator is a crucial factor in understanding and predicting the behavior of many oscillating systems in the real world, such as pendulums, springs, and electronic circuits. It is also used in fields such as engineering, physics, and mathematics to analyze and design systems that involve periodic motion.

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