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6. For small oscillations, a pendulum obeys a spring equation. Determine the general equation of motion...
A certain simple pendulum consists of a small 750.0 ? bob that swings on the end...
A certain simple pendulum consists of a small 750.0 ? bob that swings on the end of a 25.0 ?? string. The small amplitude of the oscillations of this pendulum decays to half its original value after 45.0 oscillations. The angular position of the pendulum as a function of time, ?(?), can be expressed as follows. ?(?) = ??0 ? − ??/2m cos(? ′ ? + ?) ??0 is the original angular amplitude. ? is the time, and ? is...
2. The position of the motion of the bob in a simple pendulum in radians is...
2. The position of the motion of the bob in a simple pendulum in radians is given by 0(t)-3cos What is the amplitude, frequency, and period of the motion? 3.A man enters a tall tower needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor, and its period is 12 s. How tall is the tower? Two playground swings start out together. After 5 complete oscillations, the swings are out of...
2. cm then released. A50 gram mass at rest stretches a spring by 2.5 cm. The spring is further st...
2. cm then released. A50 gram mass at rest stretches a spring by 2.5 cm. The spring is further stretched by 1.4 a) b) Assuming simple harmonic motion (with no drag), what is the frequency of the spring? If the drag coefficient r was 10 Hz, what is the frequency of the spring? If the frequency of the spring is 3 Hz, what is the drag coefficient r? c) Note: The units of the coefficient of resistance 2mr are force...
1) Amass, m, on a spring with spring constant k obeys the equation of motion Where-1...
1) Amass, m, on a spring with spring constant k obeys the equation of motion Where-1 kg. Andk is assigned a value 1 (in Sl units) What are the units of the spring constant? Assuming that at time O, the mass mis at rO traveling with a velocity of 1 m/s Work out the maximum displacement of the mass in subsequent oscillations Can you find an alternative way of getting this answer? 2) Amass,, on a spring with spring constant...
A shock absorber spring on a heavy duty truck is 21V,feet long. When installed, the spring compre...
A shock absorber spring on a heavy duty truck is 21V,feet long. When installed, the spring compresses to 2 feet. The truck weighs 7 200 1bs, so each shock absorber has a load of 1,800 lbs. Treat the compression of the spring the same as if 1,800 lbs would stretch it by 6 inches.) a What is the spring constant? b) What is the coefficient of resistance that would cause the spring to be critically damped? 4.A simple pendulum of...
(5 points) Suppose a spring with spring constant 6 N/m is horizontal and has one end...
(5 points) Suppose a spring with spring constant 6 N/m is horizontal and has one end attached to a wall and the other end attached to a 2 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 1 N.: ·s/m. a. Set up a differential equation that describes this system. Let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of...
Problem 1: For the system in figure (1-a), the spring attachment point B is given a horizontal motion Xp-b cos cut from the equilibrium position. The two springs have the same stiffness k 10 N/m and...
Problem 1: For the system in figure (1-a), the spring attachment point B is given a horizontal motion Xp-b cos cut from the equilibrium position. The two springs have the same stiffness k 10 N/m and the damper has a damping coefficient c. Neglect the friction and mass associated with the pulleys. a) Determine the critical driving frequency for which the oscillations of the mass m tend to become excessively large. b) For a critically damped system, determine damping coefficient...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force required to stretch or compress it is proportional to the distance stretched/compressed). The kinetic energy T of the system is mv2/2, where v is the velocity of the mass, and the potential energy V of the system is kr-/2, where k is the spring constant and x is the displacement of the mass from its gravitational equilibrium position. Using Lagrange's equations for mechanics (with...
The Problem The single pendulum Consider the single pendulum shown below. There is a bob at...
The Problem The single pendulum Consider the single pendulum shown below. There is a bob at the end of the pendulum, of mass T32 For soscillations in the case of a frictionless pivot and a rod with negligible mass, the motion of the pendulv time can be described by the second-order linear ODE where 0 is the angle between the rod and the vertical, g is gravity, E is the length of the rod Q1 By substituting (2) into the...
I need help with c). Question 2 The simple pendulum, discussed in week 4 and lab session 4, has the equation of motion...
I need help with c).
Question 2 The simple pendulum, discussed in week 4 and lab session 4, has the equation of motion f0/dt2_0? sin θ 9-(g/L)I/2. with The total energy of the pendulum is constant during the motion, and is given by _mgL cos θ, wher dt is the angular speed of the motion in radians per second. Consider the simple pendulum with initial conditions θ(0) and u(0)-wi, 0 i.e. starting from the vertically down position with an initial...
2. The position of the motion of the bob in a simple pendulum in radians is given by 0(t)-3cos What is the amplitude, frequency, and period of the motion? 3.A man enters a tall tower needing to know its height. He notes that a long pendulum extends from the ceiling almost to the floor, and its period is 12 s. How tall is the tower? Two playground swings start out together. After 5 complete oscillations, the swings are out of...
2. cm then released. A50 gram mass at rest stretches a spring by 2.5 cm. The spring is further stretched by 1.4 a) b) Assuming simple harmonic motion (with no drag), what is the frequency of the spring? If the drag coefficient r was 10 Hz, what is the frequency of the spring? If the frequency of the spring is 3 Hz, what is the drag coefficient r? c) Note: The units of the coefficient of resistance 2mr are force...
1) Amass, m, on a spring with spring constant k obeys the equation of motion Where-1 kg. Andk is assigned a value 1 (in Sl units) What are the units of the spring constant? Assuming that at time O, the mass mis at rO traveling with a velocity of 1 m/s Work out the maximum displacement of the mass in subsequent oscillations Can you find an alternative way of getting this answer? 2) Amass,, on a spring with spring constant...
A shock absorber spring on a heavy duty truck is 21V,feet long. When installed, the spring compresses to 2 feet. The truck weighs 7 200 1bs, so each shock absorber has a load of 1,800 lbs. Treat the compression of the spring the same as if 1,800 lbs would stretch it by 6 inches.) a What is the spring constant? b) What is the coefficient of resistance that would cause the spring to be critically damped? 4.A simple pendulum of...
(5 points) Suppose a spring with spring constant 6 N/m is horizontal and has one end attached to a wall and the other end attached to a 2 kg mass. Suppose that the friction of the mass with the floor (i.e., the damping constant) is 1 N.: ·s/m. a. Set up a differential equation that describes this system. Let x to denote the displacement, in meters, of the mass from its equilibrium position, and give your answer in terms of...
Problem 1: For the system in figure (1-a), the spring attachment point B is given a horizontal motion Xp-b cos cut from the equilibrium position. The two springs have the same stiffness k 10 N/m and the damper has a damping coefficient c. Neglect the friction and mass associated with the pulleys. a) Determine the critical driving frequency for which the oscillations of the mass m tend to become excessively large. b) For a critically damped system, determine damping coefficient...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force required to stretch or compress it is proportional to the distance stretched/compressed). The kinetic energy T of the system is mv2/2, where v is the velocity of the mass, and the potential energy V of the system is kr-/2, where k is the spring constant and x is the displacement of the mass from its gravitational equilibrium position. Using Lagrange's equations for mechanics (with...
The Problem The single pendulum Consider the single pendulum shown below. There is a bob at the end of the pendulum, of mass T32 For soscillations in the case of a frictionless pivot and a rod with negligible mass, the motion of the pendulv time can be described by the second-order linear ODE where 0 is the angle between the rod and the vertical, g is gravity, E is the length of the rod Q1 By substituting (2) into the...
I need help with c).
Question 2 The simple pendulum, discussed in week 4 and lab session 4, has the equation of motion f0/dt2_0? sin θ 9-(g/L)I/2. with The total energy of the pendulum is constant during the motion, and is given by _mgL cos θ, wher dt is the angular speed of the motion in radians per second. Consider the simple pendulum with initial conditions θ(0) and u(0)-wi, 0 i.e. starting from the vertically down position with an initial...
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