The time an object first passes a point in simple harmonic motine

In summary, the position of a mass oscillating on a spring with a frequency of 1.47 is given by x=A cos(2πt/T). If the mass is first at the position x=-.078m, then the variable t can be solved for by substituting x=-.078 into the equation. This can be done by using the inverse cosine function and solving for t. The calculator should be set to radians instead of degrees.
  • #1
cyugsi2
4
0
1. The position of a mass oscillating on a spring is given by x=(.078m)cos[2∏t/(.68s)] when is the mass first at the position x=-.078m



x=A cos(2πt/T).



3. the frequency is 1.47. I really don't know were to go from here. can anyone help me?
 
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  • #2
If you substitute x= -0.078 into the equation they gave to you, what variable can you solve for?
 
  • #3
Never mind I solved the problem I just needed to change my calculator from degree to radiants
 
  • #4
rock.freak667 said:
If you substitute x= -0.078 into the equation they gave to you, what variable can you solve for?

thanks but i just used the inverse cos.

(inverse cos(x/a)) / (2∏/2.4) = t
 
  • #5
Once you understand why you were solving for 't' in the first place :)
 

Related to The time an object first passes a point in simple harmonic motine

1. What is simple harmonic motion?

Simple harmonic motion is a type of oscillatory motion in which an object moves back and forth around a central equilibrium point, with a constant amplitude and a constant period of motion. This type of motion can be seen in many natural phenomena, such as the swinging of a pendulum or the vibration of a guitar string.

2. How is "the time an object first passes a point" related to simple harmonic motion?

In simple harmonic motion, the time an object takes to complete one full cycle of motion (known as the period) is constant. This means that the time it takes for the object to first pass a specific point will also be constant, regardless of the amplitude of the motion.

3. How is the time an object first passes a point calculated in simple harmonic motion?

The time an object first passes a point in simple harmonic motion can be calculated using the formula T = 2π√(m/k), where T is the period of motion, m is the mass of the object, and k is the spring constant of the system.

4. What factors can affect the time an object first passes a point in simple harmonic motion?

The time an object first passes a point in simple harmonic motion is primarily affected by the mass of the object and the stiffness of the system, as indicated by the formula T = 2π√(m/k). Other factors that can affect this time include the amplitude of the motion and any external forces acting on the system.

5. Can the time an object first passes a point vary in simple harmonic motion?

No, the time an object first passes a point in simple harmonic motion is constant and does not vary. This is because the period of motion remains constant in this type of motion, regardless of the amplitude or other external factors. However, the actual time value may differ for different objects or systems depending on their mass and stiffness.

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