# Aweight is attached to a spring that hangs from the ceiling of a problem 1: room. when the weight is

Aweight is attached to a spring that hangs from the ceiling of a problem 1: room. when the weight is pulled down and released, the position of the weight can be modeled using a sine or cosine function. initially, the weight hangs 40 cm from the floor. it is pulled down 10 cm and released. it takes 0.2 seconds to reach its maximum height above the floor. find an equation, using either sine or cosine, that gives the height of the weight above the floor (in cm) in terms of time. (5 points) you might want to find: the amplitude yo cof (a) the period (b) (c) the horizontal shift (optional) the vertical shift tfok (d) sketch a graph

## This Post Has 8 Comments

1. claudiagallegos26 says:

Option C.

Step-by-step explanation:

The equation that models the position of the weight and time will be a sine wave.

y = A sin(bt)

where A = amplitude of the wave

b = time period for a complete oscillation

Since b = $\frac{2\pi }{t}$

It has been given in the question, Time period t = 3 sec.

b = $\frac{2\pi }{3}$

Amplitude A = 2 in.

Now we plug in the values of amplitude and time period in the standard equation.

y = $2sin(\frac{2\pi }{3}\times t)$

y = $2sin(\frac{2\pi t}{3})$

2. jaylanmahone223 says:

The given information are:
time it takes for a single cycle - 8 seconds
distance between highest and lowest point - 20 cm

The coordinates of the first point would be
(0,0)
The coordinates of the highest points is
(2,10)
The coordinates of the midline is
(4,0)
The coordinates of the lowest point is
(6,-10)
The coordinates at time = 8 seconds is
(8,0)

3. mprjug6 says:

$T=2\pi \sqrt{\frac{m}{k} }$

Where T is the period, m is the mass of the object, and k is the spring constant. It is important to note that the amplitude of the oscillation has no effect on the period.
Which means the question should in fact say factors - the displacement will have no effect, nor will observing it in any way - the only two things there that will affect the period of the spring is changing the weight and the spring constant.

4. babyshazi says:

When t=0 the circumference is 7

5. miguelsanchez1456 says:

This graph is nonlinear

The initial displacement of the weight is 40cm

The weight first returns to equilibrium when t=1/2

Step-by-step explanation:

thats the answer i only had time to give not to explain

6. jasminespets says:

I think the most accurate answer can be the last one d. 150-137=13lb; A change in weight is positive, because the weight increases. I also think that the weight decreases each time we lose, but there's no such an answer. I think that the last word of answer d is just incorrect. The weight decreases*

7. yaniravivas79 says:

$y=2.5 \sin(\pi t)$

Step-by-step explanation:

Time period $T$ is 2 sec.

$T=\frac{2\pi}{\omega}$

$\therefore 2=\frac{2\pi}{\omega}$

$\therefore \omega=\pi$

The amplitude is half the distance between highest and lowest points.

Thus, amplitude $A= 2.5$

The equation to the SHM is:

$y=A \sin (\omega t)$

Or,

$\boxed{y=2.5 \sin (\pi t)}$

8. yay47 says:

varying the displacement of the mass from its equilibrium position

increasing the amount of time the oscillating system is observed

keeping track of the precise position of the mass through time

Explanation:

The period of a mass-spring system is given by:

$T=2 \pi \sqrt{\frac{m}{k}}$

where

m is the mass hanging from the spring

k is the spring constant

As we can see from the formula, the period depends only on these two factors: mass and spring constant, and nothing else. Therefore, the following factors do not affect the period of the system:

varying the displacement of the mass from its equilibrium position

increasing the amount of time the oscillating system is observed

keeping track of the precise position of the mass through time