Ask question

Ask question

All categories

3 years ago

10

Starting at its rightmost position, it takes 2 seconds for the pendulum of a grandfather clock to swing a horizontal distance of

18 inches from right to left and 2 seconds for the pendulum to swing back from left to right. Which of the following equations models d, the horizontal distance in inches of the pendulum from the center as a function of time, t, in seconds? Assume that right of center is a positive distance and left of center is a negative distance.
a) d=9cos(pi/4 t)
b) d=9cos(pi/2 t)
c) d=18cos(pi/4 t)
d) d=18cos(pi/2 t)

2 answers:

sdas [7]3 years ago

8 0

Answer:

The correct answer is b, x = 9 cos (pi / 2 t)

Explanation:

The equation that describes a simple pendulum is

θ = θ₀ cos (wt + φ)

The angle is measured is radians

θ = x / L

We replace

d / L = x₀ / L cos (wt + φ)

x₀ = 9 in

We replace

d = 9 cos (wt + φ)

Angular velocity is related to frequency and period.

w = 2π f = 2π / T

The period is the time of a complete oscillation T = 4 s

w =2π / 4

w = π / 2

Let's replace

x = 9 cos (π/2 t + φ)

As the system is released from the root x = x₀ for t = 0 s

x₀ = x₀ cos φ

Cos φ = 1

φ = 0°

The final equation is

x = 9 cos (pi / 2 t)

The correct answer is b

N76 [4]3 years ago

6 0

Answer:

b) d=9cos(pi/2 t)

Explanation:

This is a cosine function in the such as: y = a cos bt...

a = (maximum distance - minimum distance)/2:

a = (max - min)/2

maximum distance = 18 inches minimum distance = 0

a = (18 - 0)/2 = 18/2 = 9

That is a = 9

To solve for b, similar to the period:

The period in radians:

P = 2pi/b, which is the amount of time it takes to revolve one full cycle...

multiply that time by time from minimum to maximum, 2 to give the period as 2 × 2 = 4.

Thus to find b..

4 = 2pi/b

4b = 2pi/b × b

4b = 2pi

or

b = pi/2

Also

a = 9

b = pi/2

So our cosine function is:

d = 9cos((pi/2)t)

Hence the equation that models d

You might be interested in

A tuning fork generates sound waves with a frequency of 240 Hz. The waves travel in opposite directions along a hallway, are ref

Bingel [31]

Answer:

The phase difference between the reflected waves when they meet at the tuning fork is 159.29 rad.

Explanation:

Given that,

Frequency of sound wave = 240 Hz

Distance = 46.0 m

Distance of fork = 14 .0 m

We need to calculate the path difference

Using formula of path difference

$\Delta x=2(L_{2}-L_{1})$

Put the value into the formula

$\Delta x =2((46.0-14.0)-14.0)$

$\Delta x=36\ m$

We need to calculate the wavelength

Using formula of wavelength

$\lambda=\dfrac{v}{f}$

Put the value into the formula

$\lambda=\dfrac{343}{240}$

$\lambda=1.42\ m$

We need to calculate the phase difference

Using formula of the phase difference

$\phi=\dfrac{2\pi}{\lambda}\times \delta x$

Put the value into the formula

$\phi=\dfrac{2\pi}{1.42}\times36$

$\phi=159.29\ rad$

$\phi\approx 68.2^{\circ}$

Hence, The phase difference between the reflected waves when they meet at the tuning fork is 159.29 rad.

7 0

3 years ago

Why is this website not work how i want it this is so annoying

Mice21 [21]

It depends how you want it to work do you want to take a picture oh yea and to do that you must create a account btw

5 0

3 years ago

Read 2 more answers

Students will consider the following items: ice, glass, copper, and aluminium. what happens to each item when hammered? what pro

vladimir2022 [97]

All metals except potassium and sodium, have a property known as malleability. Malleability is the quality of something that can be shaped into something else without breaking. So when aluminium and copper are hammered they will not break. Rather they will change shape and become thin or flat at the area where its hammered.

All Non- metals except diamond are brittle in nature, so when we hammer it , they will break down into pieces. So when ice and glass will be hammered they will shatter into pieces.

4 0

3 years ago

An electron in the n = 7 level of the hydrogen atom relaxes to a lower energy level, emitting light of 397 nm. what is the value

Dimas [21]

Answer:

$n_f=2$

Explanation:

It is given that,

Initially, the electron is in n = 7 energy level. When it relaxes to a lower energy level, emitting light of 397 nm. We need to find the value of n for the level to which the electron relaxed. It can be calculate using the formula as :

$\dfrac{1}{\lambda}=R(\dfrac{1}{n_f^2}-\dfrac{1}{n_i^2})$

$\dfrac{1}{397\times 10^{-9}\ m}=R(\dfrac{1}{n_f^2}-\dfrac{1}{(7)^2})$

R = Rydberg constant, $R=1.097\times 10^7\ m^{-1}$

$\dfrac{1}{397\times 10^{-9}\ m}=1.097\times 10^7\ m^{-1}\times (\dfrac{1}{n_f^2}-\dfrac{1}{(7)^2})$

Solving above equation we get the value of final n is,

$n_f=2.04$

or

$n_f=2$

So, it will relax in the n = 2. Hence, this is the required solution.

6 0

3 years ago

Read 2 more answers

Which of the following describes sound waves?

lianna [129]

The answer is c) electromagnetic sawed in which the vibrations are perpendicular to the motion of the sound

8 0

3 years ago

Read 2 more answers