(a) Derive the Lagrange equation of motion and its solution for a simple pendulum consisting of a small bob of mass m and inextensible string of length l. Also find and sketch the total energy of such simple harmonic oscillator for the positive displacement only.

Q: A system having Lagrangian L=e" -mx The motion represented by the system is: (a) Free particle (b)…

A: In order to find the  nature of motion represented by the given lagrangian we need to find the…

Q: Simple harmonic oscillators can be used to model many different types of systems. Consider a block…

A: Given- let the block be at a height (H = 4 m) Mass of block m=2 kg As the block is in simple…

Q: Q.5) A particle is suspendended from a support by a light inextensible string which passes through a…

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Q: Find the oscillating time harmonic oscillating amplitude of 0.4m and passing through the origin with…

A: Equation of SHM  x=Aωcosωt where A is amplitude ω is angular Frequency T=2πω T is Time Period

Q: Find and find the oscillation time of an oscillator with a harmonic of amplitude 0.4m passing…

A: Amplitude is A = 0.4 m Initial velocity is v = 0.6 m/s when it passes through the origin. This is…

Q: (a) What is the amplitude of the oscillations? W

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Q: Find the amplitude, period and phase shift of the graph of y = 2sin;+)- 1, and sketch its graph over…

A: Let A denotes the amplitude, T denotes the period of the cycle, ϕ denotes the phase shift, and x…

Q: Consider a simple harmonic oscillator consisting of a one kilogram mass m' on a spring with…

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Q: A particle is dropped into a hole dug from the earth's surface to reach the surface of the earth on…

A: given a hole is dug through the centre of the earth and a particle is made to fell on it to prove…

Q: In the above question let us consider the position of mass when the spring is relaxed as x = 0, and…

A: Given: Spring constant, k = 1200 N/m Mass, m = 6 kg Displacement, A = 4.0 cm = 0.04 cm ω = 14.14…

Q: Two pendulums, both ending with mass m = 5 and with lengths l = 0.1 are coupled by a spring of…

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Q: A damped harmonic oscillator of mass m it released at time t=0 and displaced by a distance xo. Show…

A: time t=0

Q: x(t) = . which means the system is (Use integers or decimals for any numbers in the expression.…

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Q: A thin disk of radius r rolls back and forth in a spherical dish of radius R without slipping. Use…

A: When the disk rolls back and forth on a spherical dish, the disk experience a normal force, the…

Q: A mass of 4kg suspended from a light elastic string of natural length 3 feet extends it to a…

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Q: Starting from D'Alembert's principle, derive the differential equation of motion (in plane polar…

A: We know, D' Alembert's principle states that the external force is always equal to zero.…

Q: A spring/mass/dashpot system has mass 16 kg, damping constant 448 kg/sec and spring constant 5776…

A: This is a question from the waves and oscillations. Motion of any oscillating system can be…

Q: A damped harmonic oscillator of mass m it released at time t=0 and displaced by a distance xo. Show…

A: Given:  Mass of the oscillator is m. For a lightly damped (λ<<ω0) oscillator the quality…

Q: A particle is in simple harmonic motion with an amplitude of 5 cm. At time to O it passes through…

A: Solution:-Given thatAmplitude (A)=5 cmMaximum velocity (Vmax)=-12 cm/s

Q: Find the general solution for a driven, undamped harmonic oscillator with driving force Fo sin(wot).…

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Q: Find the angular frequency, amplitude, and phase angle of a particle of mass 2 gm that moves under a…

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Q: Consider a square sheet with sides: a. The sheet behaves like a compund pendulum and oscillates…

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Q: Find and find the oscillation time of an oscillator with a harmonic of amplitude 0.4m passing…

A: Amplitude, A = 0.4 mVelocity, v = 0.6 m/sTime period, t = ? SHM equation is given byx = A sin ωt

Q: One end of a spring of constant k = 9 N/s is fixed, and a mass of m = 1 kg is attached to its other…

A: Given a mass of m=1kg is attached to a spring with a spring constant of  k=9N/s. One end of the…

Q: Suppose that a mass is initially at X = Xo with an initial velocity Vo. Show that the resulting…

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Q: 4. A harmonic oscillator is made of an ideal spring with an unknown spring constant. Attached to the…

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Q: 3. A simple harmonic oscillator makes 25 complete vibrations after 5.0 seconds. Determine its (a)…

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Q: Prob.1 (1) State the required conditions of simple harmonic motion (SHH).

A: We need to find the necessary condition for simple harmonic motion.

Q: A 200-g block is attached to a horizontal spring and executes simple harmonic motion with a period…

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Q: A compressor of mass 1100 kg is mounted on a spring which deflects 10mm under the static load. The…

A: Given :                m = 1100 kg                ς = 10mm = 0.01 m                Amplitude = 6mm =…

Q: State the required conditions of simple harmonic motion (SHH). Consider the torsional pendulum with…

A: (i) There are two main conditions for a motion to be classified as SHM: The magnitude of the…

Q: A pendulum is a harmonic oscillator and suppose that once it is set into motion, it follows simple…

A: (a) The general displacement equation of a SHM is: The formula for the angular frequency is:…

Q: Find g at a point on earth where T=2.01 s for a simple pendeulum of length 1.00 m, undergoing…

A: Time period (T)=2.01 s Length(L)=1.00 m Time period==T=2πLg. Rearrange for g(acceleration due to…

Q: Write the vector function for the harmonic oscillator using the generator function, then find the…

A: The generator function for the harmonic oscillator is given by: G(u) = (mω^2/2u^2 - iu/2)^(-1/2)…

Q: 5. The amplitude of a harmonic oscillator is 5.0cm with a period of 3.0 s. The phase angle is . (a)…

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Q: A mass of 10 kgs hangs from a spring with spring constant k = 136, and is attached to a viscous…

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Q: A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h…

A: To find the frequency of the vibration of the system.

Q: The equation of motion for a damped harmonic oscillator is s(t) = Ae^(−kt) sin(ωt + δ),where A, k,…

A: Introduction: An oscillator is a system when displaced from its equilibrium position undergo a…