Simple harmonic motion (help please)

In summary: But where does the value of 0.02 r/s for w come from? That comes from the equation for circular frequency:##w=2\pi r/s##
  • #1
45
3
Homework Statement
Determinate amplitude, velocity, aceleration, and ecuation of the principal ecuations (more information in the down image)
Relevant Equations
1/T w/2pi
Captura de Pantalla 2021-04-30 a la(s) 1.58.02.png

The first ecuation values i am 99% that is correct. But, in the second and three problem i don't know if my results are ok. The problem number 2 i comprobate with the teacher that te aceleration its correct, so, with this i calculate the velocity.

I use like example the second problem for try resolve the 3rd problem, but causes me much problems.
Any help, please?
 

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  • #2
Krokodrile said:
The first ecuation values i am 99% that is correct.
Except D.

Krokodrile said:
The problem number 2 i comprobate with the teacher that te aceleration its correct, so, with this i calculate the velocity.
In a), why the +50?
In B), how did you calculate the velocity?
In C), despite your teacher's confirmation, I get a much smaller value.

Krokodrile said:
I use like example the second problem for try resolve the 3rd problem, but causes me much problems.
I don't understand how you got any of those. Please explain your reasoning.
 
  • #3
haruspex said:
Except D.In a), why the +50?
In B), how did you calculate the velocity?
In C), despite your teacher's confirmation, I get a much smaller value.I don't understand how you got any of those. Please explain your reasoning.
a) Thats my mistake, i put hz in angle.
b) The velocity: the teacher just give us the ecuation 0.1cos (314.16t+angle), i the formula v= 2pi/w: 2pi/0.02
c) Maybe I am wrong with the value copy, but i sure that say us 914.16 with m/s units.For the 3rd problem I'm on my own with a single "class", i put the values in the ecuation of the best way i can.
For the circular frecuency i used the formula w/2pi.
For the aceleration i try to work the aceleration value with pi
 
  • #4
b) have you had calculus? taking the derivative of the position x(t) will give you an equation for the velocity. The max amplitude should be apparent from that

c) m/s corresponds to a velocity, not acceleration. similar to (b) above, taking the derivative of v(t) will give you acceleration
 
  • #5
onatirec said:
b) have you had calculus? taking the derivative of the position x(t) will give you an equation for the velocity. The max amplitude should be apparent from that

c) m/s corresponds to a velocity, not acceleration. similar to (b) above, taking the derivative of v(t) will give you acceleration
Captura de Pantalla 2021-04-30 a la(s) 16.17.55.png
I tried make it better
 

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  • #6
Krokodrile said:
b) The velocity: the teacher just give us the ecuation 0.1cos (314.16t+angle), i the formula v= 2pi/w: 2pi/0.02
##100\pi## r/s is the angular velocity, which is constant. The question is asking for the maximum linear velocity, i.e. the maximum rate of change of x.
See @onatirec's advice above.
Krokodrile said:
c) Maybe I am wrong with the value copy, but i sure that say us 914.16 with m/s units.
The units are wrong for an acceleration, and if we correct the units to ##m/s^2## the number is wildly wrong. I want to know how you calculated it.
It sounds like someone gave you the answer but you wrote it down wrongly, and don't know how to find it for yourself. Is that right?
Krokodrile said:
For the circular frecuency i used the formula w/2pi.
But where does the value of 0.02 r/s for w come from?
Krokodrile said:
For the aceleration i try to work the aceleration value with pi

Here's how this stuff works:
##x(t)=A\sin(\omega t+\phi)##
Differentiate to find the velocity:
##v(t)=\frac{dx}{dt}=A\omega\cos(\omega t+\phi)##
Differentiate again to find the acceleration :
##a(t)=\frac{dv}{dt}=-A\omega^2\sin(\omega t+\phi)##

Do you understand those differentiation steps?
 

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion where an object oscillates back and forth around a central equilibrium point. It is characterized by a sinusoidal pattern and is governed by Hooke's law, which states that the restoring force acting on the object is directly proportional to its displacement from the equilibrium point.

2. What are some examples of simple harmonic motion?

Some common examples of simple harmonic motion include the swinging of a pendulum, the motion of a mass attached to a spring, and the vibrations of a guitar string. In each of these cases, the object oscillates back and forth around a central point with a constant period and amplitude.

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

Simple harmonic motion is different from other types of motion in that it is a periodic motion with a constant period and amplitude. This means that the object's motion repeats itself in a predictable pattern, unlike other types of motion such as linear or circular motion.

4. What is the equation for simple harmonic motion?

The equation for simple harmonic motion is x = A*sin(ωt + φ), where x is the displacement of the object from its equilibrium point, A is the amplitude of the motion, ω is the angular frequency, and φ is the phase angle. This equation can also be written in terms of the object's velocity and acceleration as v = A*ω*cos(ωt + φ) and a = -A*ω^2*sin(ωt + φ), respectively.

5. How is simple harmonic motion used in real life?

Simple harmonic motion is used in many real-life applications, such as in clocks and watches, musical instruments, and shock absorbers in cars. It is also used in the study of waves and vibrations, which have important applications in fields such as engineering, medicine, and seismology.

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