Simple Harmonic Motion Derivations using Calculus (Mass-Spring System)

Content Times:
0:00 Simple Harmonic Motion (SHM) Review
0:28 Mass-Spring System
1:44 The SHM Mathematical Condition
3:06 Position Equation & Phase Constant
4:28 Velocity Equation
5:37 Acceleration Equation
6:36 Showing this is SHM
7:47 Period and Angular Frequency
10:41 Period of a Mass-Spring System
11:12 Review

Next Video: Simple Pendulum - Simple Harmonic Motion Derivation using Calculus

Previous Video: Simple Harmonic Motion Creating Circular Motion from Sine and Cosine Curves

#Derivation #SimpleHarmonicMotion #SHM

[WarriorBane]

Hello sir, I just wanted to let you know I appreciate your commitment to these videos

[tannerwalston]

Great videos man just wanted to say I appreciated the effort you put in, thank you!

[qwertyuiop-ruii]

Have my physics exam in 2 hours thanks for the awesome video

[naravishthongnok]

I still have no idea why my prof. never showed us a proof for this equation, All he did was math handwaving.

[cupostuff]

How do you derive that condition for SHM

[johnedison]

Sir I love u alot love u love love u....sir r the more vidoes ....

[puns-here]

someone help me through this;
shouldn't omega in these equations be angular velocity instead of angular frequency? its a little confusing

[kon]

Just curious does this derivation apply with a vertical spring? As now the net force equation needs to account for the force of gravity?

[Paul-whnb]

To train for conditions during a manned mission on the surface of Mars, where the
acceleration due to gravity is only 3.72 m/s^2, astronauts can be hung on a spring harness
while on Earth. To provide the necessary force, we can stretch a stiff (large k) spring by a
little, or a softer (small k) spring by a lot. Should we use a stiff or soft spring to best
simulate the conditions on the Mars surface as the astronaut hops around the training ground?

Also can you help with the equations of motions for this question?

[mohfa]

Thank you for your great videos

i have question please :

What if we assumed that the acceleration (a) is in the opposite direction of (postive x) then when we apply newton's second law projecting on the positive (x direction) we would get the following equation :
- kx = - ma
ma - kx=0

Which is different differential equation than what you derived ?

Whats wrong with my logic ?, i am confused !

Thank you in advance

[seymourfroggs]

I'm sorry to say I don't like this. It's always too neat just to say omega squared just happens to be our constant when omega is defined for a separate idea. There is a better way - but I need your help - otherwise I wouldn't be here - and it is knowing from straight maths that the second derivative of sinx is -sinx and noticing that fits in here. This gets us to rotational motion without *assuming* it.

[osayieseosa]

I think I'd stick with my textbook than this video