Consider a hollow sphere (I = 2/3 M R2 when rotated about its center) of radius 0.49 m.  The sphere is pinned at its north pole (this is not its center) at allowed to undergo small oscillations about this point.  Calculate the period of the oscillation, is s, using g = 10 m/s2

Q: A double pendulum has two degrees of freedom. Produce a reasonable Lagrangian L(01, 02, 01, 02) for…

A: The required solution is following.

Q: Draw a switching circuit that represents the symbolic statement. (pv q) A (r V-s) Choose the…

A: The symbolic statement is given

Q: Calculate (a) the angular frequency and (b) the maximum displacement of the particle.

A: The mass of particle is m=2.1×10-20 kg Time period of simple harmonic motion is T=2.6×10-5 s Maximum…

Q: The figure depicts the displacement of an oscillator x[m], as a function of time t[s] 0 -1 -2 -3 0…

A: We will answer the questions by analysing the given figure. The detailed steps are given below.

Q: What is the period of oscillation (in seconds) of a rod of length 2.7m that is fixed at one end, but…

A:

Q: 11.5 * 23. A pendulum clock that ticks once per second (that being the period of one com- plete…

A: concept:

Q: iv. What is the particle's approximate SPEED at t = T/4 seconds? (for which T stands for 'Period' of…

A: Starting from mean position if time period of pendulum is T then in T/4 it will move to extreme…

Q: s Mass sliding on a Amass m is free to slide frictionlessly along the that rolls without slipping on…

A: A mass m is free to slide frictionlessly along the rim of a wheel of radius R. The wheel is…

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: The net x-force on a 1-kg oscillating object moving along the x axis is Fx = −b(x − a2x3), where b =…

A: (given) Fx=-b(x-a2x3)   b= 123 x   a=4 y The unit of "a2x3"should be "m" a2[m23] = m…

Q: Problem 1: (a) Derive the relation of the shortest wavelength limit of X-rays generated with the…

A: (a) X-rays are commonly produced  by accelerating electrons through a potential difference (a…

Q: In the following exercises assume that there's no damping.

A: Write the expression for the displacement of the mass in terms of the force and substitute the known…

Q: the mass or the carth is Me, show thnat the gravitational potential energy of a body of mass m…

A:

Q: vth in amplitude) for a direct forc- -s 100 kg and stiffness k = 2500x² N. f(t)

A: Given: The Stiffness k=2500 π2 N/m The mass of the spring mass system = 100 kg

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 uniform annular ring of mass m and inner and outer radii a and b, respectively, is pivoted around…

A:

Q: Ex. 17 Show that the velocity of a particle performing S.H.M. is half the maximum V3 of its velocity…

A: To show that-(velocity of particle)=12(maximum velocity)When, x=32a

Q: Two mass-spring systems are oscillating with the same total energy, but system A's am- plitude is…

A: Given. Two spring mass system are oscillating with same total energy. The amplitude of system a is…

Q: Consider a mechanical oscillator with the following characteristics: a mass of 3 kg, a damping…

A: Damping forces arise due to friction, viscosity, air drag, etc., and act in opposition to the…

Q: 1. In section 15.6, we derived an equation of motion for a simple pendulum where we assumed the mass…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: (c) Determine its maximum angular displacement. (For large v, and/or small /, the small angle…

A: The kinetic energy of a pendulum having maximum angular displacementis given…

Q: Consider a potential given by U(x) = -9 cos(15 x).  This potential has a stable equilibrium at x =…

A: Given: The potential is given by Ux=-9cos15x. Introduction: The time period is the time taken by a…

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

A:

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

A:

Q: Att=o, the displacenent x(o) of the mass in a mass-spring linear oscillator is-7.3 cm and the…

A: given : displacement , s = 7.8 cm = 0.078 m              acceleration, a = 2.3 m/s2

Q: In the system of Fig.(Attached), assume that m1 =1, k1 =50, k2 =10, and F0 =5 in mks units, and that…

A:

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

A:

Q: What is the period of oscillation (in seconds) of a rod of length 4.54m that is fixed at one end,…

A:

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: 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: rod of Mass (Mand lenath L=libm lis pivoted about ane end and oscillates in a . tind the Deriod of…

A: Given: Mass of the rod = M Length of rod l = 1.6 m.

Q: 7.16 A particular person’s lower leg is 56 cm long and weighs 9.5 kg. If allowed to swing freely,…

A:

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: What is the period of oscillation (in seconds) of a rod of length 4.91m that is fixed at one end,…

A: We use simple harmonic oscillation concept here to find out time period of oscillation

Q: how to find the equation to derive for part c of this problem

A: Position for simple harmonic function is given x=5.00cos2t+π6      .....(a) (b) v=dxdt…

Q: (a) Show that the potential energy of the pendulum is given by V0=mgl 1- cos 0) 10 (b) Sketch the…

A: A potential energy function is the function of the position of the object. Mathematically, a…

Q: A mass of 1 kg is suspended from a spring whose spring constant is 9 N/m. The mass is initially…

A:

Q: A pointlike body of mass m made of lead is fixed inside a homogeneous solid sphere of radius R and…

A: Given data The mass of the point-like body is m. The radius of the sphere is R The location distance…

Q: A mass of 55 grams stretches a spring by 8 cm. (Note that this means the forces balance, and thus mg…

A: m = 55 gram g = 981 m/s2 x= 8cm Initial velocity v= 23 cm/s = 0.23 m/s We can see that the particle…

Q: straight line is always acted upon by a force from the centre of the path and directed and maximum…

A: To find-(1) Maximum velocity (V)=?(2) Maximum acceleration (a)=?Given-M=8 gma=5 cmk=128 F=128 xwhere…

Q: A sphere moves in simple harmonic motion with a frequency of 1.20 Hz and an amplitude of 5.20 cm.…

A:

Q: A particle of mass m. influence of the potential energy the Sagion xze and a>0, Determine. la the…

A: The net force acting on the particle in equilibrium condition is zero. Therefore the equilibrium…

Q: A uniform rod of length 2.0 m, and 3.2 kg is suspended from a pivot a distance 0.2 m above its…

A:

Q: A ball whose mass is 1.4 kg is suspended from a spring whose stiffness is 40N/m. The ball oscillates…

A: Time period, T = 1 / f T = 1 / 0.269 Hz T = 3.717 s

Q: A cylindrical disc with a mass of 0.619 kg and radius of 0.575 m, is positioned such that it will…

A: We are given  simple harmonic motion of a physical pendulum. We have used a cylinder here. We first…