Simple Harmonic Motion and time calculation

In summary, the conversation discusses a problem involving an object undergoing simple harmonic motion with a period of 0.280 s and an amplitude of 5.95 cm. The goal is to calculate the time it takes for the object to go from x=5.95 cm to x=-1.44 cm. The equations X=A.cos(wt) and w=2pi/T are used, but the initial attempt at a solution yields an incorrect answer of 4.6 s. After realizing that the angle must be converted from degrees to radians, the correct answer is found.
  • #1
weskerq8
9
0

Homework Statement



An object is undergoing simple harmonic motion with period 0.280 s and amplitude 5.95 cm . At t=0 the object is instantaneously at rest at x= 5.95 cm.

Calculate the time it takes the object to go from x= 5.95 to x= -1.44 .

Homework Equations



X=A.cos(wt) ------> the phase angle in this case is zero (we won't worry about it)
w=2pi/T

The Attempt at a Solution



I have used the equations above ( which my teacher told me to use ) and i keep getting the wrong answer. my wrong answer came out to be 4.6 somthing...

can anyone help me find my mistake and get the real answer for this?
 
Last edited:
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  • #2
Clearly 4.6 s is not correct, if the period is .28 s.

So what angular value does ωt when it passes -1.44 ?
 
  • #3
thanks lowlypion for considering to help, actually i have solved this problem , what i was forgetting was to convert from degrees to radians. that's it :)
 
  • #4
weskerq8 said:
thanks lowlypion for considering to help, actually i have solved this problem , what i was forgetting was to convert from degrees to radians. that's it :)

Unfortunately, that's a pretty easy thing to do on some calculators.

Good luck.
 

1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion is a type of periodic motion in which an object oscillates back and forth around a central equilibrium point. This motion is characterized by a restoring force that is directly proportional to the object's displacement from the equilibrium point.

2. How is the period of SHM calculated?

The period of SHM can be calculated using the equation T = 2π√(m/k), where T is the period in seconds, m is the mass of the object in kilograms, and k is the spring constant in Newtons per meter.

3. What is the relationship between frequency and period in SHM?

The frequency of SHM is equal to the inverse of the period, or f = 1/T. This means that as the period increases, the frequency decreases and vice versa.

4. How do I calculate the time taken for an object to complete one oscillation in SHM?

The time taken for an object to complete one oscillation in SHM is equal to the period divided by the number of oscillations. This can be expressed as t = T/n, where t is the time in seconds, T is the period in seconds, and n is the number of oscillations.

5. What factors can affect the time period of an object in SHM?

The time period of an object in SHM can be affected by the mass of the object, the spring constant, and the amplitude of the oscillation. Additionally, external factors such as friction and air resistance can also impact the time period of SHM.

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