# (Not so) Simple Harmonic Motion Problem

• shurleec
In summary, a block of mass m= 0.0750 kg is attached to an unstrained horizontal spring with a spring constant of k= 82.0 N/m. The block is moved +0.120m along the +x axis and then released from rest. The force exerted by the spring on the block just before release is +9.84 N. The angular frequency of the resulting oscillatory motion is 10.5. The maximum speed of the block is 1.25 m/s and the magnitude of the maximum acceleration is 13.2 m/s^2.
shurleec

## Homework Statement

A block of mass m= 0.0750 kg is fastened to an unstrained horizontal spring whose spring constant is k= 82.0 N/m. The block is given a displacement of +0.120m, where the + sign indicates that the displacement is along the +x axis, and then released from rest.

a. What is the force (magnitude and direction) that the spring exerts on the block just before the block is released?

b. Find the angular frequency w of the resulting oscillatory motion.

c. What is the maximum speed of the block?

d. Determine the magnitude of the maximum acceleration of the block.

## Homework Equations

F= -kx
x= Acos(wt)
w= 2pif
w = (k/m)^.5
v(max)= Aw
v(sho)= -Asin(wt)
a(max)= Aw^2

## The Attempt at a Solution

a. I plugged the numbers into the equation, and got the answer + 9.84 N.
b. I plugged numbers into the equation w = (k/m)^.5 to get 10.5.
c. Since f = 1/t, I used w=2pif and set it equal to the answer in part b to solve for f, then got t. I use x = Acos(wt) to get amplitude. Then, I plugged everything into V(max) = Aw. The answer I got was 1.25m/s.
d. a(max)= Aw^2. I plugged numbers in and got 13.2m/s^2.

I'm sorry. I initially needed help, but figured it out as I was typing out my inquiries, so why waste all my work. I couldn't find this problem online at all so, yeah. [=

Welcome to PF!

Hi shurleec! Welcome to PF!

Sometimes just typing it out for someone else to see makes it all clearer!

Great job on solving the problem! Your approach and solutions seem correct. Just a couple of things to note:

- In part c, you can also use the equation v(max) = wA instead of v(max) = Aw. They are essentially the same equation, just rearranged differently.
- In part d, the units for acceleration should be m/s^2, not m/s. But the value you calculated (13.2 m/s^2) is correct.

Overall, well done on applying the equations for simple harmonic motion to solve this problem. Keep up the good work!

## 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 proportional to the displacement of the object from the equilibrium point.

## 2. What are the key components of a (Not so) Simple Harmonic Motion problem?

The key components of a (Not so) Simple Harmonic Motion problem are the mass of the object, the spring constant of the restoring force, and the initial conditions such as the amplitude, frequency, and phase angle of the motion.

## 3. How do you solve a (Not so) Simple Harmonic Motion problem?

To solve a (Not so) Simple Harmonic Motion problem, you can use the equation of motion for SHM, which is x(t) = A cos(ωt + φ), where x is the displacement of the object, A is the amplitude, ω is the angular frequency, and φ is the phase angle. You can also use energy conservation principles to solve for the maximum displacement, velocity, and acceleration of the object.

## 4. What are the differences between Simple Harmonic Motion and (Not so) Simple Harmonic Motion?

The main difference between Simple Harmonic Motion and (Not so) Simple Harmonic Motion is that (Not so) Simple Harmonic Motion problems involve additional forces or factors that affect the motion, such as damping forces, external forces, or non-ideal conditions. This makes the equations and solutions more complex and may result in different behaviors of the motion.

## 5. What are some real-life examples of (Not so) Simple Harmonic Motion?

Some real-life examples of (Not so) Simple Harmonic Motion include the motion of a mass attached to a spring and subject to air resistance, the motion of a pendulum with friction, and the motion of a car on a bumpy road. These situations involve additional forces or factors that affect the motion and make it more complex than ideal Simple Harmonic Motion.

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