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stepan [7]
3 years ago
14

A spring-mass system has a spring constant of 3 N/m. A mass of 2 kg is attached to the spring, and the motion takes place in a v

iscous fluid that offers a resistance numerically equal to the magnitude of the instantaneous velocity. If the system is driven by an external force of (21 cos 3t − 14 sin 3t) N, determine the steady state response. Express your answer in the form R cos(ωt − δ). (Let u(t) be the displacement of the mass from its equilibrium position at time t.)

Physics
1 answer:
REY [17]3 years ago
7 0

Answer:

Ut = –(√2)/6 ×Cos(3t + π/4)

Explanation:

Please see the attachments below.

This problem requires some knowledge of calculus to solve as it deals with differential equations.

The solution has been explained in detail, step by step.

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How does the balanced chemical equation show the conservation of matter in the chemical reaction?
Dmitry [639]

C. The number of F atoms in the reactants equals the number of F atoms in the products.

4 0
2 years ago
Along the line connecting the two charges, at what distance from the charge q1 is the total electric field from the two charges
Nostrana [21]

Answer:

r = d (\frac{\sqrt {q_1}}{\sqrt{q_1} + \sqrt{q_2}})

Explanation:

Here two charges are placed at distance "d" apart

now the net value of electric field at some position between two charges will be ZERO

so we will have

electric field due to charge 1 = electric field due to charge 2

E_1 = E_2

Let the position where net field is zero will lie at distance "r" from q1

\frac{kq_1}{r^2} = \frac{kq_2}{(d-r)^2}

now we will have

\frac{(d - r)^2}{r^2} = \frac{q_2}{q_1}

now square root both sides

\frac{d}{r} - 1 = \sqrt{\frac{q_2}{q_1}}

now we have

\frac{d}{r} = \sqrt{\frac{q_2}{q_1}} + 1

so we have

r = d (\frac{\sqrt {q_1}}{\sqrt{q_1} + \sqrt{q_2}})

8 0
2 years ago
An artist working on a piece of metal in his forging studio plunges the hot metal into oil in order to harden it. The metal piec
lutik1710 [3]

Answer:

The temperature of the metal is  T_m  =  376.8 ^o C

Explanation:

From the question we are told that

     The mass of the metal is  M =  60 \ kg

     The specific heat of the metal is  c_p  =  0.1027 kcal/(kg \cdot ^oC)

       The mass of the oil is M_o  =  810 \ kg

       The temperature of the oil is  T_o  =  35^oC

       The specific heat of oil is  c_o  =  0.7167 kcal/(kg \cdot ^oC )

       The equilibrium temperature is T_e  =  39 ^oC

According to the law of energy conservation

     Heat lost by metal  =  heat gained by the oil

So  

   The quantity  of heat lost by the metal is mathematically represented as

               Q =  - Mc_p \Delta T

=>            Q =  -Mc_p (T_m  -  T_c)

Where T_ m  the temperature of metal before immersion

The negative sign show heat lost

The quantity  of gained t by the metal is mathematically represented as      

           Q =  M_o c_o \Delta T

=>        Q =  M_o c_o (T_c - T_o)

So  

         Mc_p (T_m  -  T_c)   =   M_o c_o (T_c - T_o)

substituting values

          - 60 * 0.1027 (T_m  - 39)   =   810 * 0.7167 *  (39 - 35)

=>       T_m  =  376.8 ^o C

         

6 0
3 years ago
Which of the following does not cause an earthquake
antoniya [11.8K]

Answer:

C

Explanation:

A Tsunami is usually the result of an earthquake under the sea

7 0
3 years ago
The resistance of the body varies from approximately 500 kΩ (when it is very dry) to about 1.00kΩ (when it is wet). The maximum
Nady [450]

Answer:

you absolute buffoon Use Ohms' Law:   V = RI

V = (1x10^3)(5x10^-3) = 5 volts

Yes, this is in the range of normal household voltages.  

Explanation:

4 0
3 years ago
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