What if multiple forces act on an object in equilibrium??
1 answer:
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Answer:
x(t)=0.337sin((5.929t)
Explanation:
A frictionless spring with a 3-kg mass can be held stretched 1.6 meters beyond its natural length by a force of 90 newtons. If the spring begins at its equilibrium position, but a push gives it an initial velocity of 2 m/sec, find the position of the mass after t seconds.
Solution. Let x(t) denote the position of the mass at time t. Then x satisfies the differential equation
Definition of parameters
m=mass 3kg
k=force constant
e=extension ,m
ω =angular frequency
k=90/1.6=56.25N/m
ω^2=k/m= 56.25/1.6
ω^2=35.15625
ω=5.929
General solution will be
differentiating x(t)
dx(t)=-5.929c1sin(5.929t)+5.929c2cos(5.929t)
when x(0)=0, gives c1=0
dx(t0)=2m/s gives c2=0.337
Therefore, the position of the mass after t seconds is
x(t)=0.337sin((5.929t)
Answer:
They can be rank in the following way:
- A radio signal from an AM radio station at 680 kHz on the dial
- Radiation from an FM radio station at 93.1 MHz on the dial
- The red light of a light-emitting diode, such as in a calculator
- The yellow light from sodium vapor streetlights
- The gamma rays produced by a radioactive nuclide used in medical
Explanation:
The electromagnetic spectrum is the distribution of radiation due to the different frequencies at which it radiates and its different intensities, that radiation is formed by electromagnetic waves, which are transverse waves formed by an electric field and a magnetic field perpendicular to it.
Radiation is distributed along that electromagnetic spectrum according to the wavelength or frequency.
Highest frequencies
X-rays
Ultraviolet rays
Visible region
Lower frequencies
Infrared
Microwave
Radio waves
Radio waves and the visible region (yellow light, red light) are part of the electromagnetic spectrum, any radiation of that electromagnetic spectrum has a speed of 3.00x10^{8}m/s in vacuum.
However, the following equation relates the velocity, the frequency, and the wavelength:
(1)
(2)
It can be see in equation 2 that the frequency and the wavelength are inversely proportional (when the frequency increases the wavelength decreases).
Therefore, for what was already discussed, they can be rank in the next way:
- A radio signal from an AM radio station at 680 kHz on the dial
- Radiation from an FM radio station at 93.1 MHz on the dial
- The red light of a light-emitting diode, such as in a calculator
- The yellow light from sodium vapor streetlights
- The gamma rays produced by a radioactive nuclide used in medical
Summary:
In the case of the radio waves can be used:
Case for :
Case for :