Physics, 14.04.2020 18:43 alleshia2007

A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring, and the system is then immersed in a medium that offers a damping force that is numerically equal to 0.4 times the instantaneous velocity.

(a.) Find the equation of motion if the mass is initially released from rest from a
point 1 foot above the equilibrium position.

(b.) Find the first time at which the mass passes through the equilibrium position
heading upwards.

Answers: 2

Show answers

Answers

Answer from: shaylasimonds587

x(t) = e^-2t(c_1cos4t+c_2cos4t)

$x(t) = \sqrt{5}/2* e^-2tsin(4t+4.24)$

t =1.294

Explanation:

Let m be the mass attached, let k be the spring constant and let p be the positive damping constant. The Newton's second law for the system is

$md^2x/dt^2 = -kx-\beta dx/dt$

where x(t) is the displacement from the equilibrium position. The equation can be transformed into

$d^2x/dt^2 +\beta /m*(dx/dt)+k/m*x=0$

(a) Let's determine the equation of motion. We must convert units of weight into units of mass

m=W/g = 3.2/32 =1/10 slug

From Hooke's law we can calculate the spring constant k.

k = W/s = 2/1 = 2lb/ft

If we put m = 1/10 slugs, k = 2 lb/ft and $\beta$ = 0.4 into the DE, we get

d^2x/dt^2 +4*(dx/dt)+20*x=0

The auxiliary equation is m^2+4*m+20 = 0 and its solutions are m_1 = -2-4_i and m_2 = -2 + 4i. The general solution is then

x(t) = e^-2t(c_1cos4t+c_2cos4t)

From the initial conditions

x(0) = -1ft , x'(0) = 0ft/s

we can find the equation of motion

x(t) = e^-2t(-cos4t-1/2sin4t)

(b) We need to express the equation of motion in the alternative form

first attachment

The amplitude is

$A=\sqrt{c_1^2+c_2^2}=\sqrt{(-1)^2+(-1/2)^2}= \sqrt{5}/2$

and the phase angle is

sin∅= $c_1/A=-2/\sqrt{5}$

cos∅= $c_2/A=-1/\sqrt{5}$

tan∅=2

∅= $\pi +tan^-1*2$

=4.24

$x(t) = \sqrt{5}/2* e^-2tsin(4t+4.24)$

x'(t)= 5*e^-2tsin4t

The mass passes through the equilibrium when

x(t) =0

$e^-2t(-cos4t-1/2sin4t)=0\\-cos4t-1/2sin4t=0\\tan4t=-2\\4t=-tan^-1+k\pi$

t =-0.2786+k $\pi$ /4

The velocity at those times is

second attachment

The first (positive) time at which the mass passes through the equilibrium heading upward is for k = 2 (when x' < 0).

t =1.294

A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring,

Answer from: Quest

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm. the wire diameter is d = 0.9 mm. the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2) in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

Answer from: Quest

explanation:

wheres the pic

Other questions on the subject: Physics

Physics, 22.06.2019 07:00, jv910699

Hen a gfci receptacle device is installed on a 20-ampere branch circuit (12 awg copper), what is the minimum volume allowance (in cubic inches) required for conductor fill for each conductor in the outlet box?

Answers: 1

continue

Physics, 22.06.2019 14:30, tblynch21

Which of the following bonds would be most polar? a. c-i b. c-br c. c-cl d. c-f e. c-o

Answers: 1

continue

Physics, 22.06.2019 16:00, 6FOOT

The electric potential v is constant everywhere within a certain region of space. which statement below is true? the choices are: the electric field is also constant (but not zero) within the region. a charged particle placed within the region will experience an electric force. the electric field is zero everywhere within the region. the electric field varies from place to place within the region.

Answers: 2

continue

Physics, 22.06.2019 17:30, realoneree

This chart shows characteristics of three different types of waves. which statement is best supported by the information in the chart? wave x and wave y are mechanical waves, and wave z is an electromagnetic wave. wave x and wave y are electromagnetic waves, and wave z is a mechanical wave. wave x and wave z are electromagnetic waves, and wave y is a mechanical wave. wave x and wave z are mechanical waves, and wave y is an electromagnetic wave.

Answers: 1

continue

You know the right answer?

A force of 2 pounds stretches a spring 1 foot. A mass weighing 3.2 pounds is attached to the spring,...