Please help with simple harmonic motion

Therefore, the period of simple harmonic motion for the pendulum in case (a) is:T = 2\pi \sqrt{\frac{l}{g+a}}And for case (b):T = 2\pi \sqrt{\frac{l}{\sqrt{g^2 + a^2}}}For the second part of the conversation, the equation for maximum amplitude without slipping is:A_{max} = \frac{\mu_s g}{w^2}where \mu_s is the coefficient of static friction, g is the acceleration due to gravity, and w is the angular frequency.
  • #1
cissablecat23
9
0
1a)A simple pendulum is 4.35 m long. What is the period of simple harmonic motion for this pendulum if it is hanging in an elevator that is accelerating upward at 5.90 m/s2?


b)What is the period of simple harmonic motion for this pendulum if it is placed in a truck that is accelerating horizontally at 5.90 m/s2?

2) A large block P executes horizontal simple harmonic motion as it slides across a frictionless surface with a frequency of f = 1.52 Hz. Block B rests on it, as shown in the figure below, and the coefficient of static friction between the two is μs = 0.630.

What maximum amplitude of oscillation can the system have if block B is not to slip?

1)l=4.35 m
a= 5.90 m/s/s

w^2=g/l
w^2=9.80/4.35
w^2= 2.252873563

then i have to find T.. but i don't know what formula to use...

2) w=2(pie)f
w-2(pie)(1.52 Hz)
w= 9.5504
and i don't know what else to do
 
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  • #2
1)

T= 2pi * sqrt(L/g)
T= 2pi* sqrt(4.35 m/ [9.8m/s^2-5.90m/s^2])

2)

"as shown in the figure below" <- picture?
 
  • #3
it was a picture with a big block on the bottom.. a small block on the top.. with a spring attached to it..

i got the first part of the question.. it was T=2pi sqrt(l/g+a)

but i cannot get the second part of it... with it acclerating horizontally..
 
  • #4
springs? I thought we were talking about pendulums?! I can't visualize #2
 
  • #5
#2 is different from #1... it's.. a small block on a big block.. and the big block has a spring attached to it.. the coefficient of static friction was..0.630.. they want to know what's the maximum amplitude of the oscillation so that the little block doesn't slip..

f= 1.52 Hz

AND for #1.. if they change the a from upward.. to horizontal.. how does that change the answer...
 
  • #6
spring attached to it where? On the bottom? sides? Need to be specific

I don't think the answer for #1 changes
 
  • #7
i've got it.. thanks.. :)
 
  • #8
Are you sure it's 2 pi ( sqrt ( L / (g - a ) ) ? Or is it g + a?
 
  • #9
cissablecat23 said:
1a)A simple pendulum is 4.35 m long. What is the period of simple harmonic motion for this pendulum if it is hanging in an elevator that is accelerating upward at 5.90 m/s2?


b)What is the period of simple harmonic motion for this pendulum if it is placed in a truck that is accelerating horizontally at 5.90 m/s2?
In a non-accelerating frame, the period of a simple pendulum is:
[tex]T = 2\pi \sqrt{\frac{l}{g}}[/tex]
In an accelerating frame, the effective "g" is different.

For case (a), the apparent acceleration is [itex]-g\hat{y} -a\hat{y} = -(g+a)\hat{y}[/itex], so [itex]g_{eff} = g + a[/itex].

For case (b), the apparent acceleration is [itex]-g\hat{y} -a\hat{x}[/itex], so [itex]g_{eff} = \sqrt{g^2 + a^2}[/itex].
 

1. What is simple harmonic motion?

Simple harmonic motion is a type of periodic motion in which an object oscillates back and forth around an equilibrium point, with a restoring force proportional to the displacement from the equilibrium point. This type of motion can be observed in many everyday phenomena, such as the swinging of a pendulum or the vibrations of a guitar string.

2. What are the key characteristics of simple harmonic motion?

The key characteristics of simple harmonic motion include a constant period or time for one complete oscillation, a sinusoidal or wave-like motion, and a constant amplitude or maximum displacement from the equilibrium point.

3. How is simple harmonic motion related to Hooke's law?

Hooke's law states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position. This relationship is also seen in simple harmonic motion, where the restoring force is proportional to the displacement from the equilibrium point.

4. What is the formula for calculating the period of simple harmonic motion?

The formula for calculating the period of simple harmonic motion is T = 2π√(m/k), where T is the period, m is the mass of the object, and k is the spring constant.

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

Compared to other types of motion, simple harmonic motion is characterized by a restoring force that is proportional to the displacement, resulting in a sinusoidal or wave-like motion. Other types of motion, such as linear or circular motion, may have different forms of restoring forces and resulting motions.

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