In a simple harmonic motion, when the displacement is one-half the amplitude. what fraction of the total energy is kinetic? (d) 1/4. Show
When the displacement of a body making SHM is half of its amplitude the fraction of KE to the total energy is?What fraction of the total energy is K.E. when the displacement is one half of a amplitude of a particle executing S.H.M? Kinetic energy is equal to three fourth (i. e. 34) of the total energy, when the displacement is one-half of its amplitude. When the displacement in SHM is one third of the amplitude? Ans. (L=0.9910 m) 0.25. When the displacement in S.H.M. is one third of the amplitude, what fraction of total energy is Kinetic and P.E. 1 K.E. 8. 1/16 When the displacement in SHM is one third of the amplitude what fraction of total energy is kinetic?Therefore, kinetic energy is 89 of total energy and potential energy is 19 of total energy. At what displacement is the energy half kinetic and half potential? Answer: At what displacement from the mean position its energy is half kinetic and half potential. when Kinetic energy is maximum potential energy is zero. when kinetic energy is half of its maximum, potential energy will become other half and both are equal. What happens to the energy of a simple harmonic oscillator if its amplitude is doubled?Statement 1: If the amplitude of a simple harmonic oscillator is doubled, its total energy becomes four times. Statement 2: The total energy is directly proportional to the square of the amplitude of vibration of the harmonic oscillator. What is potential energy SHM?The sum of the kinetic and potential energies in a simple harmonic oscillator is a constant, i.e., KE+PE=constant. Moreover, the energy is proportional to the amplitude squared of the motion. The kinetic energy attains its maximum value, and the potential energy attains it minimum value, when the displacement is zero. At what distance from the mean position in SHM The energy is half kinetic and half potential? At what displacement from the mean position its energy is half kinetic and half potential. when Kinetic energy is maximum potential energy is zero. when kinetic energy is half of its maximum, potential energy will become other half and both are equal. At what time PE is half of the total energy?Solution. The time in which the potential energy will be half of total energy is 1.25 s. At what distance from the mean position is the kinetic energy?Answer Expert Verified The distance x from its mean position may be specified as: x = A cos (wt+Ф), A is the amplitude and Ф is the phase constant, t is time. NOW, x = A /√2, So, when the body is at 1/√2 th of its amplitude then the PE = KE. At what distance from mean position kinetic energy is 3 times potential energy? At amplitude the kinetic energy experienced is given by total mechanical energy conservation. By the question the kinetic energy of the particle at a particular amplitude is thrice its potential energy, i.e., I.e., the condition is satisfied if the particle reaches half of its maximum amplitude. At what distance from the mean position is the speed of a particle performing SHM half?answer=since, path lenght is 10 cm,so A=5cm(half of path length). V=Vmax/2=wa/2…. (since half its maximum speed) At what position is the kinetic energy equal to the potential energy?When the kinetic energy is maximum, the potential energy is zero. This occurs when the velocity is maximum and the mass is at the equilibrium position. The potential energy is maximum when the speed is zero. Why does kinetic energy decrease with height? As the height increases, there is an increase in the gravitational potential energy P and a decrease in the kinetic energy K. The kinetic energy K is inversely proportional to the height of the object. What is the relationship of mass into the kinetic energy?Kinetic energy is directly proportional to the mass of the object and to the square of its velocity: K.E. = 1/2 m v2. If the mass has units of kilograms and the velocity of meters per second, the kinetic energy has units of kilograms-meters squared per second squared. How does the kinetic energy of a moving body depend on its speed and mass?(i) Kinetic energy of a moving body is directly proportional to the square of the speed of the moving body. (ii) Kinetic energy of a moving body is directly proportional to the mass of the moving body. RelatedAnswer  Hint:We are asked to find out how much part of total energy is potential energy and kinetic energy. First recall the formulas for total energy and potential energy in S.H.M or simple harmonic motion, use those to find out the part of total energy which is potential energy. Then use conservation of energy to find out the part for kinetic energy. Complete step by step answer: Given, displacement is one-third of amplitude. Let \[A\] be the amplitude of the S.H.M, then displacement will be\[x = \dfrac{1}{3}A\] ………(i)Total energy in S.H.M is given as,\[T.E = \dfrac{1}{2}m{\omega ^2}{A^2}\] ……………(ii)Where \[m\] is the mass of the particle executing S.H.M, \[\omega \] is the frequency and \[A\] is the amplitude.To find out what fraction of total energy is potential energy, let’s find out the potential energy. Potential energy in S.H.M is given as,\[P.E = \dfrac{1}{2}m{\omega ^2}{x^2}\]Putting the value of \[x\] in the above equation we get,\[P.E = \dfrac{1}{2}m{\omega ^2}{\left( {\dfrac{A}{3}} \right)^2} \\\Rightarrow P.E = \dfrac{1}{2}m{\omega ^2}\dfrac{{{A^2}}}{9} \\\Rightarrow P.E = \dfrac{1}{9}\left( {\dfrac{1}{2}m{\omega ^2}{A^2}} \right) \]Now, substituting equation (ii) in the above equation we get,\[P.E = \dfrac{1}{9}\left( {T.E} \right)\] ……....(iii)Therefore, we observe that potential is \[\dfrac{1}{9}\] of total energy.From conversation of energy we get,\[K.E + P.E = T.E\] …...(iv)where \[K.E\] is the kinetic energy.Now substituting the value of potential energy from equation (iii) in equation (iv), we get\[K.E + \dfrac{1}{9}\left( {T.E} \right) = T.E \\\Rightarrow K.E = T.E - \dfrac{1}{9}\left( {T.E} \right) \\\therefore K.E = \dfrac{8}{9}T.E \]Therefore, kinetic energy is \[\dfrac{8}{9}\] of total energy and potential energy is \[\dfrac{1}{9}\] of total energy. Note:S.H.M or Simple harmonic motion is a type of oscillatory motion and also periodic. In case of S.H.M the restoring force is directly proportional to the displacement from the mean position. One important point you should remember is that all S.H.M are oscillatory motions but all oscillatory motions may not be S.H.M. |
When the displacement in SHM is one third of the amplitude the fraction of the kinetic energy to total energy is?
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