Displacement and acceleration ( SHM? )

In summary: A stone is thrown from a distance of 3m, so that it will hit the child at the base of the line when it has traveled a distance of 2.5m. What is the displacement of the child when the stone is thrown?In summary, the displacement of the child when the stone is thrown is 2.5m.
  • #1
Vandetah
13
0

Homework Statement


A small body is undergoing simple harmonic motion on a frictionless horizontal surface with an amplitude of 0.13m. At a point 0.05 m from equilibrium the velocity is 0.24 m/s. a.) what is the period?
What is the displacement and acceleration when the velocity is ±0.10 m/s




Homework Equations



T = 2∏ √[itex]\frac{l}{g}[/itex]

Displacement = [itex]\frac{a}{\frac{-4∏^{2}}{T^{2}}}[/itex]

acceleration = [itex]\frac{v^{2}}{A}[/itex]



The Attempt at a Solution



T = 2∏ √[itex]\frac{0.05m}{g}[/itex]

T = 0.45 S

Displacement = [itex]\frac{0.08 m/s^{2}}{\frac{-4∏^{2}}{0.45 S^{2}}}[/itex]
= -4.10 x [itex]10^{-4}[/itex] m

acceleration = [itex]\frac{0.10m/s^{2}}{0.13m}[/itex]
= 0.08 m/[itex]s^{2}[/itex]


how is it?
 
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  • #2
Vandetah said:

Homework Statement


A small body is undergoing simple harmonic motion on a frictionless horizontal surface with an amplitude of 0.13m. At a point 0.05 m from equilibrium the velocity is 0.24 m/s. a.) what is the period?
What is the displacement and acceleration when the velocity is ±0.10 m/s




Homework Equations



T = 2∏ √[itex]\frac{l}{g}[/itex]

This is the wrong equation. This is the equation for the period of oscillation of a pendulum of length l. Since the object in your problem is oscillating horizontally, g is not going to come into it.
 
  • #3
so the other two equation looks good except for the period?

i dnt think i can use 2∏√[itex]\frac{m}{k}[/itex] ??
 
  • #4
There are particular expressions for position vs. time, velocity vs. time, and acceleration vs. time that apply to SHM. To me, using these is the quickest way to solve the problem.
 
  • #5
the basic equations? like:

a = [itex]\frac{Δv}{t}[/itex]

displacement = vt

v = [itex]\frac{d}{t}[/itex]
 
  • #6
Vandetah said:
the basic equations? like:

a = [itex]\frac{Δv}{t}[/itex]

displacement = vt

v = [itex]\frac{d}{t}[/itex]

No, of course not. These equations don't describe oscillation. Can you think of functions that do?
 
  • #7
so the relevant equations i mentioned in the op has nothing to do with the problem statement?
 
  • #8
Vandetah said:
A small body is undergoing simple harmonic motion on a frictionless horizontal surface with an amplitude of 0.13m. At a point 0.05 m from equilibrium the velocity is 0.24 m/s. a.) what is the period?
What is the displacement and acceleration when the velocity is ±0.10 m/s

Start with the expression of the displacement as function of time in case of simple harmonic motion. Do you know it?

http://hyperphysics.phy-astr.gsu.edu/hbase/shm.html


ehild
 

1. What is displacement in SHM?

Displacement in SHM (simple harmonic motion) refers to the distance an object moves from its equilibrium position. It is a measure of the object's position in relation to its starting point.

2. How is displacement related to acceleration in SHM?

In SHM, displacement and acceleration are directly proportional. This means that as displacement increases, acceleration also increases. This relationship is described by the equation a = -ω²x, where a is acceleration, x is displacement, and ω is the angular frequency.

3. What is the difference between displacement and amplitude in SHM?

Displacement and amplitude are both measures of distance in SHM, but they have different meanings. Displacement refers to the distance an object has moved from its equilibrium position, while amplitude refers to the maximum displacement of an object from its equilibrium position. Amplitude is always equal to or greater than displacement.

4. How does the mass of an object affect its displacement in SHM?

The mass of an object does not affect its displacement in SHM. The displacement of an object in SHM is determined by its initial conditions, such as its starting position and velocity, as well as the forces acting upon it, such as the restoring force and any external forces.

5. How is SHM used in real-life applications?

SHM has many real-life applications, such as in pendulums, springs, and musical instruments. It is also used in engineering and physics to model and understand the behavior of vibrating systems, such as bridges, buildings, and electronic circuits.

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