Simple harmonic motion, finding displacement given time

In summary, the problem requires finding the position of a mass at t=1.00s using the given equation x(t) = (7.40cm)cos[(4.16s^-1)t - 2.42]. The attempt at a solution involved converting 7.40cm to 0.074m and checking units and unit conversions. Despite finding the velocity and acceleration, the correct position was not obtained initially due to incorrect sig figs. The actual answer was -0.0125m.
  • #1
scholio
160
0

Homework Statement



mass = 1.8kg
given equation in problem x(t) = (7.40cm)cos[(4.16s^-1)t - 2.42]
*when i tried solving i converted 7.40cm to 0.074m

find the position of the mass at t = 1.00s

Homework Equations



x(t) = (7.40cm)cos[(4.16s^-1)t - 2.42]

The Attempt at a Solution



i've been working on this problem for a while, i haven't been able to get the correct answer, even when i made sure to check units and make necessary unit conversions. i made sure my units were in radians (within the cosine) but it keeps yielding the wrong answer, i was able to find velocity and acceleration from the given equation, just not position.

i thought this problem would be just plug and chug, when i stuck t=1.00s it still hasn't given me the correct answer, i got -0.01 and 0.074, both were incorrect

thanks
 
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  • #2
EDIT sorry for double posting - actually was kinda correct the first time, it was just very picky with sig figs, i initially entered -0.01 which was incorrect, the actual answer was -0.0125
 
  • #3
for any help!

I would suggest double checking your calculations and making sure all units are consistent. It is possible that there may be a small error in your calculations that is causing the incorrect answer. It may also be helpful to try using a calculator or computer program to solve the equation, as it can be more accurate. Additionally, it may be helpful to plot the equation on a graph to visualize the motion and see if the result makes sense. If the issue persists, it may be helpful to consult with a teacher or classmate for further assistance.
 

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which a particle moves back and forth along a straight line, with a restoring force that is directly proportional to the displacement from the equilibrium position. Examples of simple harmonic motion include a mass attached to a spring and a pendulum swinging back and forth.

2. What is the equation for displacement in simple harmonic motion?

The equation for displacement in simple harmonic motion is x = A sin(ωt + φ), where x is the displacement, A is the amplitude (maximum displacement), ω is the angular frequency, and φ is the phase angle.

3. How do you find the displacement given time in simple harmonic motion?

To find the displacement given time in simple harmonic motion, you can use the equation x = A sin(ωt + φ). Plug in the values for the amplitude, angular frequency, and phase angle, and then solve for x.

4. What is the relationship between period and frequency in simple harmonic motion?

The period of a simple harmonic motion is the time it takes for one complete cycle, while the frequency is the number of cycles per unit time. The relationship between period and frequency is T = 1/f, where T is the period and f is the frequency.

5. Can the displacement in simple harmonic motion ever be negative?

Yes, the displacement in simple harmonic motion can be negative. This occurs when the particle moves in the opposite direction from its equilibrium position. The equation x = A sin(ωt + φ) allows for both positive and negative values of x.

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