Find the periodic-time (T) of a simple pendulum if its natural frequency ωn= 54 rad / sec and length is 2 m.
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- Find the periodic-time (T) of a simple pendulum if its natural frequency ωn= 54 rad / sec and length is 2 m.

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- The position of an oscillating object in cm is described by x = (3) cos 8πt, where t is in seconds. Find the first time the particle reaches the equilibrium position after the oscillation has started.What must be the length of a simple pendulum if its oscillationfrequency is to be equal to that of an air-track glider of mass 0.350 kgattached to a spring of force constant 8.75 N/m?Let the spring have a mass of 191.3 +/- 01g. A 75+/- 01 g mass is attached to the spring. The mass is displaced 1/2 inch and released from rest. After fitting the position data with a sine fit, the position amplitude is found to be 0.0146+/- 0.0003 M. A) calculate the angular frequency of the mass (with uncertainty) b) Determine the amplitude of the velocity of the mass (with uncertainty) c) Find the amplitude of the acceleration (with uncertainty)
- A ball of mass 0.05 kg vibrates back and forth from the free end of an ideal spring having a force constant of 50 N/m. If amplitude of the motion is 0.10 m what is the kinetic energy of the ball when it is 0.04 m from its equilibrium postion.A 0.20 kg ball is tied to a string. It is pulled to an angle of 8.00º and released to swing as a pendulum. At student with a stopwatch finds that 10 oscillations take 12 s. How long is the string? Use g = 10 m/s/s.(a) (b) (c) (d) The figure below shows a pendulum with length L and the angle 0 from the vertical to the pendulum. It can be shown that 0, as a function of time, satisfies the following nonlinear differential equation d²0 g dt² L where g denotes the acceleration due to gravity. + sin 0 0 For small values of 0 we can assume de dt A 0 sin 0 L such that the differential equation can be considered to be linear. Find the equation of motion of the pendulum with length 750 cm if 0 is initially 15° and its initial angular velocity is = 1 rad/s. What is the maximum angle from the vertical? What is the period of the pendulum (the time to complete one back-and-forth swing)? When will the pendulum be vertical from initial position, that is, 0 = 0 ?