# simple harmonic motion derivation class 11

Reading Time: 9min read 0. So those who are looking for preparation and planing to cover whole physics syllabus quickly must go with our Notes. x As we displace it towards right, spring force will try to bring mass m towards left. When particle is at mean position, y = o.

A motion which repeats itself identically after a fixed interval of time is called periodic motion. (-ive sign shows it is pointing towards the centre of the circle.). It is defined as the distance from mean position (XX1 of O) of a body executing SHM. The acceleration is maximum where velocity is minimum and vice-versa. 4) The component mgsin$\theta$ is not perfectly directed towards mean position. The motion is sinusoidal in time and demonstrates a single resonant frequency. The above graph shows displacement as a continuous function of time. The Organic Chemistry Tutor 135,673 views Under thissituation the spring on the left side getselongated by a length equal to x and that onthe right side gets compressed by the samelength. Your IP: 69.64.58.60 Hence, motion of a simple pendulum is SHM. a p = -ω 2 r where r = radius; Consider a particle moving in a circular path. Show that when the mass is displaced from its equilibrium position on either side, it executes a simple harmonic motion. Simple Harmonic Motion (SHM) is a periodic motion the body moves to and fro about its mean position.The restoring force on the oscillating body is directly proportional to its displacement and is always directed towards its mean position. Simple Harmonic Motion (SHM) is a periodic motion the body moves to and fro about its mean position.The restoring force on the oscillating body is directly proportional to its displacement and is always directed towards its mean position. (g on the surface of earth is 9.8 ms–2), Answer: -Acceleration due to gravity on the surface of moon,g' = 1.7 m s–2, Acceleration due to gravity on the surface of earth, g = 9.8 m s–2, Time period of a simple pendulum on earth, T = 3.5 s. The length of the pendulum remains constant, On moon’s surface, time period, T’= 2π√l/g’.

Consider a particle moving in a circular path. The quantity θ = ωt + Φ is called the phase. 25. of the bob is called point of oscillation. Let us consider a body of mass ‘m’ is connected at one end of a thread of length ‘l’ which passes through a rigid support at point O. In addition, other phenomena can be approximated by simple harmonic motion, including the motion of a simple pendulum as well as molecular vibration. We can derive the time period for the mass spring system by as we know, ${\omega ^2} = \frac{{\rm{k}}}{{\rm{m}}}$, Where $\omega$ is the angular velocity, if T is the time of oscillation, then, $\omega {\rm{\: }} = \frac{{2{\rm{\pi }}}}{{\rm{T}}}$, $\omega {\rm{\: }} = \frac{{2{\rm{\pi }}}}{{\rm{T}}}$ = $\sqrt {\frac{{\rm{K}}}{{\rm{m}}}}$, Here, T= $2{\rm{\pi }}\sqrt {\frac{{\rm{m}}}{{\rm{K}}}} {\rm{\: }}$. Consider a particle moving in circular path. It is known as radial acceleration. Let the mass be displaced by a smalldistance x to the right side of the equilibriumposition, as shown in Fig (a). Then the device is called simple pendulum. At t = 1.5 s, calculate the (a) displacement,(b) speed and (c) acceleration of the body? Acceleration in uniform circular motion always directed towards the centre. It is known as radial acceleration. Necessary and sufficient conditions for a motion to be simple harmonic: It is an oscillatory motion (to and fro) in which acceleration of a body is directly proportional to displacement and acceleration is always directed towards fixed point (Mean position). • Let us displace spring by a distance towards right. A particle executing S.H.M., the maximum potential energy in same as that of maximum kinetic energy which is equal to total energy: ${{\rm{E}}_{\rm{k}}} = \frac{1}{2}{\rm{m}}{{\rm{v}}^2}$, $= \frac{1}{2}{\rm{m}}{{\rm{w}}^2}\left( {{{\rm{r}}^2} - {{\rm{y}}^2}} \right)$, ${{\rm{E}}_{\rm{p}}} = \frac{1}{2}{\rm{k}}{{\rm{y}}^2}$, $= \frac{1}{2}{\rm{m}}{{\rm{w}}^2}{{\rm{r}}^2}$, Total energy of the particle at any point is, E = ${{\rm{E}}_{\rm{p}}} + {{\rm{K}}_{\rm{E}}}$, $= 2{\rm{\: m\: }}{{\rm{r}}^2}{{\rm{f}}^2}{\rm{\: \: }}{{\rm{r}}^2}{\rm{\: }}$, i. Here, acceleration is directly proportional to displacement and they are opposite to each other. Simple Pendulum Equation - Frequency, Period, Velocity, Kinetic Energy - Harmonic Motion Physics - Duration: 1:07:11. SHM is the projection of the uniform circular motion such that centre of uniform circular motion becomes the mean position of the SHM and the radius of the circular motion is the amplitude of the SHM. We know that if we stretch or compress the spring, the mass will oscillate back and forth about its equilibrium (mean) position. Find the period of oscillations? When particle is at extreme position, y = r. And total energy is equal to the maximum value of P.E. Cloudflare Ray ID: 5f82e2511d924941

Hence, the time period of the simple pendulum on the surface of moon is 8.4 s. (a) Time period of a particle in SHM depends on the force constant k and mass m of the particle: T = 2π√ (m/k). The component mgsin$\theta$ provides restoring force to move the bob towards mean position. If we plot the graph between displacement versus time we can conclude that the displacement is continuous function of time. In right angle $\Delta$OPM, sin$\theta$ = OM/OP = y/r or, y = rsin$\theta$, We know, angular velocity, $\omega$ = $\frac{\theta }{{\rm{t}}}$∴$\theta$ =${\rm{\: }}\omega$t.

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