What is the resulting angular frequency of the oscillation?

In summary, the conversation discusses finding the angular frequency of a mass hanging from a spring with a given spring constant, after being displaced from equilibrium and released. The formula used to find the period, T, is 2∏sqrt(m/k), where m is the mass and k is the spring constant. The correct formula for finding the angular frequency, ω, is 2∏/T. The mistake in the solution was not including the mass, 0.65 kg, in the formula for the period.
  • #1
jimmyboykun
39
0

Homework Statement



A 0.65-kg mass is hanging from a spring with spring constant 15 N/m. Then the mass is displaced from the equilibrium by 2 cm and let go.

Homework Equations



angular frequency:ω=2∏/T

The Attempt at a Solution



I found T: 2∏sqrtm/k, 2∏sqrt0.02/15N/m= 0.229429488s

ω=2∏/0.229429488s=27.39rad/s

I got the answer wrong but the units are suppose to be in rad/s. I feel like 0.65kg plays a role in the equation, but don't know where to place it. Where exactly did I go wrong.
 
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  • #2
jimmyboykun said:

Homework Statement



A 0.65-kg mass is hanging from a spring with spring constant 15 N/m. Then the mass is displaced from the equilibrium by 2 cm and let go.

Homework Equations



angular frequency:ω=2∏/T

The Attempt at a Solution



I found T: 2∏sqrtm/k, 2∏sqrt0.02/15N/m= 0.229429488s

ω=2∏/0.229429488s=27.39rad/s

I got the answer wrong but the units are suppose to be in rad/s. I feel like 0.65kg plays a role in the equation, but don't know where to place it. Where exactly did I go wrong.

Take a look at the formula you used to find the period, T. What are the variables involved?

(also, make use of parentheses to delineate the argument of a function like sqrt(...) so we can tell what you're taking the square root of )
 

1. What is angular frequency?

Angular frequency is a measure of how quickly an object is rotating or oscillating around a fixed point. It is represented by the symbol ω (omega) and is measured in radians per second.

2. How is angular frequency related to frequency and period?

Angular frequency is directly related to frequency and period, which are measures of how many times an object completes a full rotation or oscillation in a given time period. The angular frequency is equal to 2π times the frequency, or 2π divided by the period.

3. What factors affect the resulting angular frequency of an oscillation?

The resulting angular frequency of an oscillation is affected by the mass, stiffness, and length of the oscillating object. It is also affected by any external forces acting on the object, such as gravity or friction.

4. How is angular frequency calculated?

Angular frequency can be calculated using the formula ω = 2π/T, where ω is the angular frequency and T is the period of the oscillation.

5. How does angular frequency differ from linear frequency?

Angular frequency is a measure of rotational or oscillatory motion, while linear frequency is a measure of straight-line motion. Angular frequency is measured in radians per second, while linear frequency is measured in cycles per second (Hertz).

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