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Leni [432]
2 years ago
13

An object hangs from a spring in a stable (equilibrium) position. The spring is pulled 3 feet downward and the object begins to

oscillate, making one complete oscillation every 4 seconds. What is an equation of the motion of this object
Physics
1 answer:
mote1985 [20]2 years ago
5 0

The equation of the motion of this object is  \mathbf{y = 3 cos \Big [ \dfrac{ \pi}{2}(t -2) \Big ] }

<h3>What is oscillation?</h3>

An oscillation in a waveform is a periodic set of vibrations an object in the medium produces.

From  the parameters given:

  • The spring is pulled 3 feet down ward from the origin(equilibrium position) = -3
  • Time to complete one oscillation = 4 seconds

The angular velocity can be computed by using the formula:

\mathbf{\omega = \dfrac{2 \pi}{T}}

\mathbf{\omega = \dfrac{2 \pi}{4.0}}

The amplitude A from the oscillation is:

\mathbf{\Big|A \Big| = \Big|\dfrac{3 - (-3)}{2} \Big| = 3}

It implies that the vertical shift (D) is:

\mathbf{\dfrac{minimum + maximum}{2} = \dfrac{3+(-3)}{2} = 0}

However, by using the formula of the general form of a sinusoidal equation, we have:

\mathbf{y = A cos \Big [ \dfrac{2 \pi}{4}(t -2) \Big ] + 0}

\mathbf{y = 3 cos \Big [ \dfrac{ \pi}{2}(t -2) \Big ] }

Learn more about oscillation in waveform here:

brainly.com/question/15701473

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The smallest detail visible with ground-based solar telescopes is about 1 arc second. How large a region (in km) does this repre
mestny [16]

Answer:

x = 727.5 km

Explanation:

With the conditions given using trigonometry, we can find the tangent

       tan θ = CO / CA

With CO the opposite leg and CE is the adjacent leg which is the distance from the Tierral to Sun

   

        D =150 10⁶ km (1000m / 1 km)

        D = 150 10⁹ m.

We must take the given angle to radians.

       1º  = 3600 arc s  

       π rad = 180º

       θ = 1 arc s (1º / 3600 s arc) (pi rad / 180º) =

       θ = 4.85 10⁻⁶ rad

That angle is extremely small, so we can approximate the tangent to the angle

     

       θ = x / D

       x = θ D

       x = 4.85 10-6  150 109

       x = 727.5 103 m

       x = 727.5 km

4 0
3 years ago
two forces whose magnitude are in ratio of 3:5 gives a resultant of 35N.if the angle of inclination is 60degree.calculate the ma
nadya68 [22]

Answer:

the magnitude of first force = 3 × 5= 15 N

ANd, the magnitude of second force = 5 × 5 = 25 N

Explanation:

The computation of the magnitude of the each force is shown below:

Provided that

Ratio of forces = 3: 5

Let us assume the common factor is x

Now

first force =  3x

And, the second force = 5x

Resultant force = 35 N

The Angle between the forces = 60 degrees  

Based on the above information

Resultant force i.e. F = √ F_1^2 +F_2^2 + 2 F_1F_2cos\theta

35 = √[(3x)²+ (5x)²+ 2 (3x)(5x) cos 60°]

 35 =√ 9x² + 25x² + 15x²    (cos 60° = 0.5)

35 = √49 x²

 x = 5

So, the magnitude of first force = 3 × 5= 15 N

ANd, the magnitude of second force = 5 × 5 = 25 N

7 0
3 years ago
The magnetic field at the equator points north. If you throw a positively charged object (for example, a baseball with some elec
PilotLPTM [1.2K]

Answer:

The magnetic force points in the positive z-direction, which corresponds to the upward direction.

Option 2 is correct, the force points in the upwards direction.

Explanation:

The magnetic force on any charge is given as the cross product of qv and B

F = qv × B

where q = charge on the ball thrown = +q (Since it is positively charged)

v = velocity of the charged ball = (+vî) (velocity is in the eastern direction)

B = Magnetic field = (+Bj) (Magnetic field is in the northern direction; pointing forward)

F = qv × B = (+qvî) × (Bj)

F =

| î j k |

| qv 0 0|

| 0 B 0

F = i(0 - 0) - j(0 - 0) + k(qvB - 0)

F = (qvB)k N

The force is in the z-direction.

We could also use the right hand rule; if we point the index finger east (direction of the velocity), the middle finger northwards (direction of the magnetic field), the thumb points in the upward direction (direction of the magnetic force). Hence, the magnetic force is acting upwards, in the positive z-direction too.

Hope this Helps!!!

5 0
2 years ago
What do you mean by kinetic energy and potential energy ?
Verizon [17]

  • Kinetic Energy of an object is the measure of the work an object can do by virtue of its motions..

  • Formula - KE = 1/2 mv^2

  • Where KE is the kinetic energy, m is the body’s mass, and v is the body’s velocity.

  • Potential energy is the stored energy in any object or system by virtue of its position or arrangement of parts..

  • Formula - W = mgh

Where,

. m is the mass in kilograms

. g is the acceleration due to gravity

. h is the height in meters

Hope it helpz~ uh..

4 0
1 year ago
Find the slit separation of a double-slit arrangement that will produce interference fringes 0.018 rad apart on a distant screen
inessss [21]

Answer:

1.64 * 10^(-5) m

Explanation:

Parameters given:

Angular separation, θ = 0.018 rad

Wavelength, λ = 589 nm = 5.89 * 10^(-7) m

The angular separation when there are 2 slots is given as

θ = λ/2d

where d = separation between slits

d = λ/2θ

d = (589 * 10^(-9))/(2 * 0.018)

d = 1.64 * 10^(-5) m

5 0
2 years ago
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