Find position after t for simple harmonic motion

In summary, the conversation involves a 28.0 kg block connected to a wall via a spring on a frictionless air track. The block is pushed to a position of x=0.350 m and released, resulting in simple harmonic motion with a period of 4.70 s. The question is then asked about the position of the block after 3.854 s. The equations used to solve for this position are T=2pi*sqrt(m/k), KE1+PE1=KE2+PE2, x=Asin(omega*t), and omega=2pi*frequency. The amplitude A is given as 0.35 m and is plugged into the equation to solve for x, resulting in an incorrect
  • #1
smillphysics
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0
A 28.0 kg block at rest on a horizontal frictionless air track is connected to the wall via a spring. The equilibrium position of the mass is defined to be at x=0. Somebody pushes the mass to the position x= 0.350 m, then let's go. The mass undergoes simple harmonic motion with a period of 4.70 s. What is the position of the mass 3.854 s after the mass is released?

T=2pi*sqrt m/k
KE1+PE1=KE2+PE2 from this you get mv^2=KA^2
x=Asin *omega*t
omega=2pi*frequency
frequency =1/T

I used the first equation get k=3.92
then I use that k in the second equation, but I don't know how to get v to then get A. Any help? Would I then take that A and plug it into the third equation to get my X?
 
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  • #2
In the given problem the amplitude A is given. ( 0.35 m). Find x.
 
  • #3
So I plugged in A (.35m) into the equation,
x=.35sin(1.34*3.854) and got x=.032 which is still incorrect? Any help on where I am going wrong?
The second part of this problem calls for the maximum acceleration- would I use the equation a=omega^2cos omega *t? I don't think that I will get this problem correct if I got the last one incorrect.
 
  • #4
Your formula for posistion does not work at t=0! You need a phase angle in it, or use cosine instead of sine.
 
  • #5
I figured this problem out. Thank you!
 

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around a central equilibrium point. This type of motion is characterized by a smooth, sinusoidal curve and is often seen in systems with a restoring force, such as a mass attached to a spring or a pendulum.

2. How do you calculate the position of an object after a certain time in simple harmonic motion?

The position of an object in simple harmonic motion can be calculated using the equation x = A cos(ωt + φ), where x is the position, A is the amplitude, ω is the angular frequency, and φ is the phase angle. To find the position after a certain time t, simply plug in the value for t into the equation.

3. What factors affect the position of an object in simple harmonic motion?

The position of an object in simple harmonic motion is affected by three main factors: the amplitude, the angular frequency, and the phase angle. The amplitude determines the maximum displacement of the object from its equilibrium position, while the angular frequency determines the rate at which the object oscillates. The phase angle determines the starting point of the motion.

4. Can the position of an object in simple harmonic motion be negative?

Yes, the position of an object in simple harmonic motion can be negative. This occurs when the object is on the opposite side of the equilibrium position from where it started. The position can be negative or positive depending on the direction of the motion.

5. How is the period of simple harmonic motion related to the angular frequency?

The period of simple harmonic motion is inversely proportional to the angular frequency. This means that as the angular frequency increases, the period decreases. The period is the time it takes for the object to complete one full oscillation, while the angular frequency is the number of oscillations per unit time.

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