Simple harmonic frequency clarification

In summary, the frequency of oscillation of the mass attached to a massless spring with a spring constant of 23.5 N/m is 13.90 Hz. This is calculated using the formula f=(1/2pi)[sqroot(k/m)] where k is the spring constant and m is the mass of the attached body. Make sure to input the correct values in the formula and use the correct units for accurate results.
  • #1
Rasine
208
0
A massless spring with spring constant 23.5 N/m hangs vertically. A body of mass 0.30 kg is attached to its free end and then released. Assume that the spring was unstretched before the body was released.

What is the frequency of oscillation of the resulting motion, assumed to be simple harmonic?

ok so f=(1/2pi)[sqroot(k/m)] because w=sqroot(k/m) and f=w/2pi

so i have (1/2pi)[sqroot(23.5/.30)] which is 13.90...right?

and the units would be Hz right becuase w is in rad/s and that divided by rad would give cycles/s


i think i am doing something wrong. please point it out to me.
 
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  • #2
Rasine said:
so i have (1/2pi)[sqroot(23.5/.30)] which is 13.90...right?

Your thinking and your equation are OK. Maybe your calculator is broken :smile:

Hint: my calculator says sqrt(23.5/0.3) = 8.85
 
  • #3
thats what i get too but the formula says that 8.85 should be divided by 2pi which is 13.90

is that calculation right? should i do that?
 
  • #4
On my calculator 8.85 x PI / 2 = 13.90. I guess you are pushing the wrong buttons.

2pi is about 6.28. There is no way that 8.85/6.28 could be 13.90 !
 

What is simple harmonic frequency?

Simple harmonic frequency is a type of oscillation or vibration that occurs when a system is displaced from its equilibrium position and experiences a restoring force proportional to the displacement. This results in a repetitive motion with a constant frequency.

What is the equation for simple harmonic frequency?

The equation for simple harmonic frequency is f = 1/T = (1/2π) * √(k/m), where f is the frequency, T is the period, k is the spring constant, and m is the mass of the system.

What is the difference between frequency and period in simple harmonic motion?

Frequency is the number of cycles or oscillations that occur in one second, while period is the time it takes for one complete cycle or oscillation to occur. They are inversely related, meaning that as frequency increases, period decreases.

What are some real-life examples of simple harmonic motion?

Some examples of simple harmonic motion include a swinging pendulum, a mass attached to a spring, and a vibrating guitar string. These systems all experience a restoring force that is proportional to their displacement from equilibrium, resulting in simple harmonic motion.

How is simple harmonic frequency related to resonance?

Resonance occurs when a system is exposed to a periodic force at its natural frequency. In simple harmonic motion, the natural frequency is the same as the frequency of the oscillation. Therefore, resonance can occur in systems experiencing simple harmonic motion when they are exposed to an external force at the same frequency.

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