Homework Answers
SHM graphs
When we plot the displacement, velocity and acceleration during SHM against time we get the graphs below.
The velocity equation simplifies to the equation below when we just want to know the maximum speed.
The acceleration equation simplifies to the equation below when we just want to know the maximum acceleration.
Time period of a mass-spring system
Time period of a Pendulum
SHM and Energy
For a pendulum undergoing SHM energy is being transferred back and forth between kinetic energy and potential energy. The total energy remains the same and is equal to kinetic energy + potential energy (see graph below).
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The period for oscillation of the cart is given by T = Sketch a graph of...
Homework for Lab 15: Simple Harmonic Motion Name Date Section 15 10 -5 -15-10-5 0 5...
Homework for Lab 15: Simple Harmonic Motion Name Date Section 15 10 -5 -15-10-5 0 5 10 15 Displacement (em) Figure 15.6: Force vs displacement graph for a 0.75 kg cart on a horizontal spring. 1. Figure 15.6 shows the force exerted by the spring on a 0.75 kg cart, as a function of its displacement from equilibrium. Positive displacements (in cm) represent stretching of the spring; negative displacements represent compression. Find the spring constant. 2. The cart is moved...
Homework: Simple Harmonic Motion Name: 1. A 4.5-kg block is hung from a spring causing the...
Homework: Simple Harmonic Motion Name: 1. A 4.5-kg block is hung from a spring causing the spring to elongate 12 cm. (a) What is the spring constant for this spring? (b) If the spring was stretched 18 cm and released, what will be the period of oscillation? 2. What mass on a spring with a spring constant of 160 N/m will oscillate with a period of 2.0 s? 3. A mass of 240 g oscillates on a spring on a...
5) A damped simple harmonic oscillator consists of a.40 kg mass oscillating vertically on a spring...
5) A damped simple harmonic oscillator consists of a.40 kg mass oscillating vertically on a spring with k- 15 N/m with a damping coefficient of .20 kg/s. The spring is initially stretched 17 cm downwards and the mass is released from rest. a) What is the angular frequency of the mass? b) What is the position of the mass at t-3 seconds? c) Sketch a position vs time graph for the mass, showing at least 5 full cycles of oscillation....
(6) O Y 25 cm FIGURE 4 FIGURE 4 shows a bead executing a simple harmonic...
(6) O Y 25 cm FIGURE 4 FIGURE 4 shows a bead executing a simple harmonic motion with a period of 1.8 s, along a straight line between points, X and Y which are 25 cm apart. Point O is at midpoint between X and (i) Write an equation for the displacement of the bead. (ii) Calculate the magnitude of acceleration of the bead point P. (b) A 25 kg block connected to one end of a string is displaced...
A 0.60 kg block rests on a frictionless horizontal countertop, where it is attached to a...
A 0.60 kg block rests on a frictionless horizontal countertop, where it is attached to a massless spring whose k-value equals 18.0 N/m. Let x be the displacement, where x = 0 is the equilibrium position and x > 0 when the spring is stretched. The block is pushed, and the spring compressed, until xi = −4.00 cm. It then is released from rest and undergoes simple harmonic motion. (a)What is the block's maximum speed (in m/s) after it is...
Consider the force-displacement graph for a spring shown. Determine the spring constant, the potential energy stored...
Consider the force-displacement graph for a spring shown. Determine the spring constant, the potential energy stored when the spring is stretched from x = 0 to x = 4.0 cm. the change in the potential energy stored in stretching the spring from x = 1.0 cm to x = 4.0 cm. A cart having a mass M = 180 g on a friction free horizontal surface is accelerated from rest by the launching spring of problem 2. What is the...
M A spring connects a fixed wall to the top of the uniform cylinder on a...
M A spring connects a fixed wall to the top of the uniform cylinder on a horizontal surface. Originally the spring is horizontal, and it is neither extended nor compressed. The cylinder is rolled slightly to one side, and released from rest. The cylinder rolls without slipping on the surface, and the centre of mass follows a simple harmonic oscillator. You can treat the spring as being horizontal throughout the motion. The mass of the cylinder is M, the radius...
A spring has an unstretched length of 12 cm. When an 80 g ball is hung...
A spring has an unstretched length of 12 cm. When an 80 g ball is hung from it, the length increases by 4.0 cm. Then the ball is pulled down another 4.0 cm and released. Draw a position-versus-time graph showing the motion of the ball for three cycles of the oscillation. Let the equilibrium position of the ball be y=0. Be sure to include appropriate units on the axes so that the period and the amplitude of the motion can...
1. An air-track cart attached to s spring completes one oscillation every 2.4 s. At t...
1. An air-track cart attached to s spring completes one oscillation every 2.4 s. At t = 0 the cart is released from rest at a distance of 0.10 m from its equilibrium position. What is the position of the cart at (a) 2.7s and (b) 3.0s? (c) What is the first time the car is at position x = -5.0 cm? I WWWWWWWWWWWW r=-0.10 m 0 x = 0.10 m The pendulum in a grandfather clock is designed to...
Homework for Lab 15: Simple Harmonic Motion Name Date Section 15 10 -5 -15-10-5 0 5 10 15 Displacement (em) Figure 15.6: Force vs displacement graph for a 0.75 kg cart on a horizontal spring. 1. Figure 15.6 shows the force exerted by the spring on a 0.75 kg cart, as a function of its displacement from equilibrium. Positive displacements (in cm) represent stretching of the spring; negative displacements represent compression. Find the spring constant. 2. The cart is moved...
Homework: Simple Harmonic Motion Name: 1. A 4.5-kg block is hung from a spring causing the spring to elongate 12 cm. (a) What is the spring constant for this spring? (b) If the spring was stretched 18 cm and released, what will be the period of oscillation? 2. What mass on a spring with a spring constant of 160 N/m will oscillate with a period of 2.0 s? 3. A mass of 240 g oscillates on a spring on a...
5) A damped simple harmonic oscillator consists of a.40 kg mass oscillating vertically on a spring with k- 15 N/m with a damping coefficient of .20 kg/s. The spring is initially stretched 17 cm downwards and the mass is released from rest. a) What is the angular frequency of the mass? b) What is the position of the mass at t-3 seconds? c) Sketch a position vs time graph for the mass, showing at least 5 full cycles of oscillation....
(6) O Y 25 cm FIGURE 4 FIGURE 4 shows a bead executing a simple harmonic motion with a period of 1.8 s, along a straight line between points, X and Y which are 25 cm apart. Point O is at midpoint between X and (i) Write an equation for the displacement of the bead. (ii) Calculate the magnitude of acceleration of the bead point P. (b) A 25 kg block connected to one end of a string is displaced...
Consider the force-displacement graph for a spring shown. Determine the spring constant, the potential energy stored when the spring is stretched from x = 0 to x = 4.0 cm. the change in the potential energy stored in stretching the spring from x = 1.0 cm to x = 4.0 cm. A cart having a mass M = 180 g on a friction free horizontal surface is accelerated from rest by the launching spring of problem 2. What is the...
M A spring connects a fixed wall to the top of the uniform cylinder on a horizontal surface. Originally the spring is horizontal, and it is neither extended nor compressed. The cylinder is rolled slightly to one side, and released from rest. The cylinder rolls without slipping on the surface, and the centre of mass follows a simple harmonic oscillator. You can treat the spring as being horizontal throughout the motion. The mass of the cylinder is M, the radius...
1. An air-track cart attached to s spring completes one oscillation every 2.4 s. At t = 0 the cart is released from rest at a distance of 0.10 m from its equilibrium position. What is the position of the cart at (a) 2.7s and (b) 3.0s? (c) What is the first time the car is at position x = -5.0 cm? I WWWWWWWWWWWW r=-0.10 m 0 x = 0.10 m The pendulum in a grandfather clock is designed to...
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