Simple Harmonic Motion: Finding displacement at given time t

In summary, the conversation discusses finding the position of a 1.10 kg mass on a spring at t=1.00s using the displacement equation x(t)=(7.40cm)cos[(4.16rad/s)t−2.42rad]. After encountering an incorrect answer, it is discovered that the incorrect calculator mode (degrees instead of radians) was the cause. The conversation ends with the realization that this mistake is common and can happen to anyone.
  • #1
Vanessa Avila
94
1

Homework Statement


A 1.10 kg mass on a spring has displacement as a function of time given by the equation
x(t)=(7.40cm)cos[(4.16rad/s)t−2.42rad].

Find the position of the mass at t=1.00s;

Homework Equations


x = Acos(ωt+∅)

The Attempt at a Solution


I tried to just plug in the time t in that equation to solve for the displacement, but I'm getting 0.074 which apparently is not the right answer:

x = 0.0740m*cos(4.16rad/s(1.00s) - 2.42rad)
x = 0.074
 
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  • #2
Is your calculator's mode set for degrees or radians?
 
  • #3
aha! it's in degrees!
gneill said:
Is your calculator's mode set for degrees or radians?
 
  • #4
Vanessa Avila said:
aha! it's in degrees!
:smile:
 
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  • #5
gneill said:
:smile:
Thanks a lot lol. I didn't catch that at all. I'm so stupid XD
 
  • #6
Vanessa Avila said:
Thanks a lot lol. I didn't catch that at all. I'm so stupid XD
Eh. It happens more often than you might think, and to some very clever people, too!
 
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FAQ: Simple Harmonic Motion: Finding displacement at given time t

1. What is Simple Harmonic Motion (SHM)?

Simple Harmonic Motion is a repetitive back-and-forth movement that occurs when a restoring force is applied to an object. The motion follows a sinusoidal pattern and is characterized by a constant amplitude and frequency.

2. How do you calculate displacement in SHM at a given time t?

The displacement in SHM at a given time t can be calculated using the equation x(t) = A*cos(ωt + φ), where x(t) is the displacement, A is the amplitude, ω is the angular frequency, and φ is the phase angle.

3. What is the difference between amplitude and displacement in SHM?

The amplitude in SHM is the maximum displacement from the equilibrium position, while the displacement is the actual distance from the equilibrium position at a specific time t.

4. Can the displacement ever be greater than the amplitude in SHM?

No, the displacement in SHM can never exceed the amplitude. The amplitude is the maximum displacement, and the object will always return to its equilibrium position after one complete cycle of motion.

5. How does the period of SHM affect the displacement at a given time t?

The period of SHM, which is the time it takes for one complete cycle of motion, does not affect the displacement at a given time t. The displacement is solely dependent on the amplitude, angular frequency, and phase angle.

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