The amount of energy carried by a wave is related to the amplitude of the wave. A body free to rotate about an axis can make angular oscillations. Spark transmitters could not transmit audio (sound) and instead transmitted information by radiotelegraphy, the operator tapped on a telegraph key which turned the transmitter on and off to produce pulses of radio waves spelling out text messages in Morse code. Transmitters must be licensed by governments, under a variety of license classes depending on use such as broadcast, marine radio, Airband, Amateur and are restricted to certain frequencies and power levels. Surface waves, in this mechanical sense, are commonly known as either Love waves (L waves) or Rayleigh waves. From healthy diet plans to helpful weight loss tools, here you'll find WebMD's latest diet news and information. The negative sign shows that the force is in the opposite direction. All Rights Reserved, Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that which is only imaginary.The term is also used to refer to the ontological status of things, indicating their existence. Practical frequency modulation (FM) transmission was invented by Edwin Armstrong in 1933, who showed that it was less vulnerable to noise and static than AM. The alternating voltage will also charge the ends of the conductor alternately positive and negative, creating an oscillating electric field around the conductor. The two times that differ are the apparent solar time, which directly tracks the diurnal motion of the Sun, and mean solar time, which tracks a theoretical mean Sun with uniform motion along the celestial equator. Read latest breaking news, updates, and headlines. A simple form of interference pattern is obtained if two plane waves of the same frequency intersect at an angle. In electronics and telecommunications, a radio transmitter or just transmitter is an electronic device which produces radio waves with an antenna.The transmitter itself generates a radio frequency alternating current, which is applied to the antenna.When excited by this alternating current, the antenna radiates radio waves. In the US, both the creation and subjects of motion pictures began to reflect second-wave feminist ideals, leading to the development of feminist film theory. (2)\end{array} \), \(\begin{array}{l}v =\frac{dx}{dt}=\omega \sqrt{{{A}^{2}}-{{x}^{2}}}\end{array} \), \(\begin{array}{l}\Rightarrow \int{\frac{dx}{\sqrt{{{A}^{2}}-{{x}^{2}}}}}=\int\limits_{0}^{t}{\omega dt}\end{array} \), \(\begin{array}{l}\Rightarrow {{\sin }^{-1}}\left( \frac{x}{A} \right)=\omega t+\phi\end{array} \), \(\begin{array}{l}\Rightarrow {{\sin }^{-1}}\left( \frac{{{x}_{0}}}{A} \right)=\phi\end{array} \), \(\begin{array}{l}{{\sin }^{-1}}\left( \frac{O}{A} \right)=\phi\end{array} \), \(\begin{array}{l}\Rightarrow {{\sin }^{-1}}\left( \frac{A}{A} \right)=\phi\end{array} \), \(\begin{array}{l}\Rightarrow {{\sin }^{-1}}\left( 1 \right)=\phi\end{array} \), \(\begin{array}{l}\text{We can find particles, displacement}\ \left( \overrightarrow{x} \right), \text{velocity}\ \left( \overrightarrow{v} \right) \text{and acceleration as follows}.\end{array} \), \(\begin{array}{l}v = \frac{d}{dt}A\sin \left( \omega t+\phi \right)=\omega A\cos \left( \omega t+\phi \right)\end{array} \), \(\begin{array}{l}v = A\omega \sqrt{1-{{\sin }^{2}}\omega t}\end{array} \), \(\begin{array}{l}\frac{{{x}^{2}}}{{{A}^{2}}}={{\sin }^{2}}\omega \,t\end{array} \), \(\begin{array}{l}\Rightarrow v = A\omega \sqrt{1-\frac{{{x}^{2}}}{{{A}^{2}}}}\end{array} \), \(\begin{array}{l}\Rightarrow v = \omega \sqrt{{{A}^{2}}-{{x}^{2}}}\end{array} \), \(\begin{array}{l}\Rightarrow {{v}^{2}}={{\omega }^{2}}\left( {{A}^{2}}-{{x}^{2}} \right)\end{array} \), \(\begin{array}{l}\Rightarrow \frac{{{v}^{2}}}{{{\omega }^{2}}}=\left( {{A}^{2}}-{{x}^{2}} \right)\end{array} \), \(\begin{array}{l}\Rightarrow \frac{{{v}^{2}}}{{{\omega }^{2}}{{A}^{2}}}=\left( 1-\frac{{{x}^{2}}}{{{A}^{2}}} \right)\end{array} \), \(\begin{array}{l}\Rightarrow \frac{{{v}^{2}}}{{{A}^{2}}}+\frac{{{v}^{2}}}{{{A}^{2}}{{\omega }^{2}}}=1\end{array} \), \(\begin{array}{l}\overrightarrow{a}=\frac{dv}{dt}=\frac{d}{dt}\left( A\omega \cos \omega t+\phi \right)\end{array} \), \(\begin{array}{l}\Rightarrow \overrightarrow{a}=-{{\omega }^{2}}A\sin \left( \omega t+\phi \right)\end{array} \), \(\begin{array}{l}\Rightarrow \left| a \right|=-{{\omega }^{2}}x\end{array} \), \(\begin{array}{l}v = A\omega \cos \left( \omega t+\phi \right)=\omega \sqrt{{{A}^{2}}-{{x}^{2}}}\end{array} \), \(\begin{array}{l}a = -A{{\omega }^{2}}\sin \left( \omega t+\phi \right)=-{{\omega }^{2}}x\end{array} \), \(\begin{array}{l}\text{the displacement}\ \left( \overrightarrow{x} \right),\ \text{velocity}\ \left( \overrightarrow{v} \right)\ \text{and acceleration}\ \left( \overrightarrow{a} \right)\ \text{at any time t are given by}\end{array} \), \(\begin{array}{l}a = -{{\omega }^{2}}A\sin \left( \omega t+\phi \right)=-{{\omega }^{2}}x\end{array} \), \(\begin{array}{l}\text{The restoring force}\ \left( \overrightarrow{F} \right)\ \text{acting on the particle is given by}\end{array} \), \(\begin{array}{l}=\frac{1}{2}m{{v}^{2}}\ \left[ Since, \;{{v}^{2}}={{A}^{2}}{{\omega }^{2}}{{\cos }^{2}}\left( \omega t+\phi \right) \right]\end{array} \), \(\begin{array}{l}=\frac{1}{2}m{{\omega }^{2}}{{A}^{2}}{{\cos }^{2}}\left( \omega t+\phi \right)\end{array} \), \(\begin{array}{l}=\frac{1}{2}m{{\omega }^{2}}\left( {{A}^{2}}-{{x}^{2}} \right)\end{array} \), \(\begin{array}{l}=\frac{1}{2}m{{\omega }^{2}}{{A}^{2}}{{\cos }^{2}}\left( \omega t+\phi \right)=\frac{1}{2}m{{\omega }^{2}}\left( {{A}^{2}}-{{x}^{2}} \right)\end{array} \), \(\begin{array}{l}w = \int{dw}=\int\limits_{0}^{x}{-kxdx=\frac{-k{{x}^{2}}}{2}}\end{array} \), \(\begin{array}{l}= -\frac{m{{\omega }^{2}}{{x}^{2}}}{2}\end{array} \), \(\begin{array}{l}\left[ \,k=m{{\omega }^{2}} \right]\end{array} \), \(\begin{array}{l}= -\frac{m{{\omega }^{2}}}{2}{{A}^{2}}{{\sin }^{2}}\left( \omega t+\phi \right)\end{array} \), \(\begin{array}{l}=\frac{m{{\omega }^{2}}{{x}^{2}}}{2}=\frac{m{{\omega }^{2}}{{A}^{2}}}{2}{{\sin }^{2}}\left( \omega t+\phi \right)\end{array} \), \(\begin{array}{l}E = \frac{1}{2}m{{\omega }^{2}}\left( {{A}^{2}}-{{x}^{2}} \right)+\frac{1}{2}m{{\omega }^{2}}{{x}^{2}}\end{array} \), \(\begin{array}{l}E = \frac{1}{2}m{{\omega }^{2}}{{A}^{2}}\end{array} \), \(\begin{array}{l}\overrightarrow{{{a}_{c}}}=A{{\omega }^{2}}\end{array} \), \(\begin{array}{l}{{a}_{N}}=A{{\omega }^{2}}{{\sin }^{2}}\left( \omega t+\phi \right)\end{array} \), \(\begin{array}{l}{{a}_{L}}=A{{\omega }^{2}}{{\cos }^{2}}\left( \omega t+\phi \right)\end{array} \), Difference betweenPeriodic, Oscillation andSimple Harmonic Motion, Simple Harmonic Motion Equation and its Solution, Solutions ofDifferential Equations of SHM, Conditions for an Angular Oscillation to be Angular SHM, Equation of Position of a Particle as a Function of Time, Necessary conditions for Simple Harmonic Motion, Velocity of a particle executing Simple Harmonic Motion, Total Mechanical Energy of the Particle Executing SHM, Geometrical Interpretation of Simple Harmonic Motion, Problem-Solving Strategy in Horizontal Phasor, Frequently Asked Questions on Simple Harmonic Motion, Test your knowledge on 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