Simple harmonic motion problem

In summary, the problem involves a mass of 346 g on a spring with a constant of 26.8 N/m on a horizontal and frictionless surface, with an amplitude of 6.7 cm. The first two parts were successfully solved, finding the total energy to be 0.0601526 J and the maximum speed to be 0.58966337 m/s. In part 3, the question is to find the magnitude of the velocity when the displacement is equal to 3.6 cm. Using the energy from part 1, the calculation yielded a velocity of 0.4904863694 m/s, which was found to be incorrect due to an error in the highlighted term. Once corrected, the
  • #1
DLH112
20
0

Homework Statement


This is a 3 part problem and I've successfully solved the first 2 parts, but I don't know what I did wrong in the third part.

1) mass of 346 g on a spring with constant 26.8 N/m on a horizontal + frictionless surface.
Amplitude is 6.7 cm. In part 1 i found the total energy to be 0.0601526 J. and in part 2 i found the max speed to be 0.58966337 m/s.

part 3 is "What is the magnitude of the velocity of the mass when the displacement is equal to 3.6 cm? answer in m/s"

Homework Equations


E = KE + PE , 1/2KA^2 = 1/2kx^2 + 1/2mv^2


The Attempt at a Solution


using the energy from part 1 as E...
0.0601526 = (0.5)(26.8)(0.036)^2 + (0.5)(0.346)v^2
0.061526 = 0.0185328 + (0.5) (0.346)v^2
0.0416198 = (0.5)(0.346)v^2
0.2405768786 = v^2
0.4904863694 m/s = V ... is apparently wrong
 
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  • #2
DLH112 said:
using the energy from part 1 as E...
0.0601526 = (0.5)(26.8)(0.036)^2 + (0.5)(0.346)v^2
0.061526 = 0.0185328 + (0.5) (0.346)v^2
Double check the highlighted term.
 
  • #3
ah thank you. i was accidentally using 28.6 instead of 26.8.
 

Related to Simple harmonic motion problem

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where an object oscillates back and forth around an equilibrium point. The motion follows a sinusoidal pattern and is characterized by a constant frequency and amplitude.

2. How is simple harmonic motion different from other types of motion?

Simple harmonic motion is unique in that it is a purely restoring force motion, meaning that the force acting on the object is proportional to the displacement from the equilibrium point. This results in a sinusoidal motion that repeats itself over time.

3. What are some common examples of simple harmonic motion?

Some common examples of simple harmonic motion include the motion of a pendulum, a mass on a spring, and a vibrating guitar string. These systems all exhibit oscillatory motion around a central equilibrium point.

4. How is the period of simple harmonic motion related to its frequency?

The period of simple harmonic motion is the time it takes for one complete cycle of the motion. It is inversely proportional to the frequency, meaning that as the frequency increases, the period decreases. This relationship is represented by the equation T = 1/f, where T is the period and f is the frequency.

5. How do you solve a simple harmonic motion problem?

To solve a simple harmonic motion problem, you first need to identify the known and unknown variables, such as the mass, spring constant, amplitude, and frequency. Then, you can use the equations of motion, such as x = A sin(ωt) and F = -kx, to solve for the unknown variable. It is also important to consider conservation of energy and the conditions for simple harmonic motion, such as negligible damping and small amplitudes.

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