Mass and Spring: A 3.4 kg mass hangs in equilibrium from a spring. When the mass is displaced by 0.08 m and released from rest, it reaches a top speed of 2.5 m/s as it oscillates. A group of students records the motion of the spring for 242 seconds and deduces the system has a quality factor of Q = 4520. (a) What is the period of oscillation? (b) What is the spring constant of the spring?
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- Consider a pendulum whose length is 50 ft. What is the formula for the period of oscillation for a pendulum? (Use the following as necessary: L for the length of the pendulum and g for the acceleration of gravity. Do not substitute numerical values; use variables only.) T = 2π₁ X Determine the period in s. 7.8 ✔ S g What is the formula that shows the relationship between the natural frequency and the period of oscillation? (Use the following as necessary: T. Do not substitute numerical values; use variables only.) f = t X Determine the natural frequency in Hz. 0.128 ✔ HzAn experiment conducted with the pendulum on Earth has a period of 2.00 seconds, and we know that the acceleration due to gravity is 9.8 m/s. An astronaut took the same pendulum to the moon during a space mission to experiment on the moon. Where the acceleration due to gravity is 1.67m/s', what is its period on the moon?In the distance future, data from the oscillation of a pendulum with a length of 2.1 cm and a mass of 630 g was collected from a planetary rover sent to the surface of planet HIP130446 in the Andromeda galaxy. The data from the ocillation of the pendulum is presented below. Oscillating Pendulum amplitude (cm) time (s) 14 12 0.333 4 10 0.500 8. 0.667 12 8 0.833 8 1.000 4 4 1.167 8 1.333 12 1.500 8 0.5 1 1.5 2 2.5 3.5 4 1.667 1.833 8. time (seconds) 2.000 12 2.167 8. 2.333 4 distance (cm) 3)
- Problem 2: A 0.49-kg mass suspended from a spring undergoes simple harmonic oscillations with a period of 1.4 s. How much mass, in kilograms, must be added to the object to change the period to 1.9 s? Numeric : A numeric value is expected and not an expression. Am =In a spring-mass experiment, a hanging spring is stretched by 5 cm when a mass of 156 g object is attached to it. When the mass is put to oscillate, the sensor measured a maximum speed of 3.84 m/s. Take g = 9.8 m/s². b) What is the spring constant value? At what position(s) will the object have a speed 1/2 that of the maximum speed? Take y = 0 at the equilibrium and upward is a positive direction. At t = 0, the object is moving at 1/2V max away from the equilibrium with the spring compressed. Using y (t) = A cos(wt + 0), write a complete expression with numerical values and units to describe the motion of the object.A pendulum has a length of 0.00272 m. What is the period of its oscillation?
- A 0.214-kg ball is hung vertically from a spring. The spring stretches by 3.44 cm from its natural length when the ball is hanging at equilibrium. A child comes along and pulls the ball down an additional 5cm, then lets go. How long (in seconds) will it take the ball to swing up and down exactly 4 times, making 4 complete oscillations before again hitting its lowest position? Hints: This question contains more information than necessary. Also, beware of unit conversions!A 52.6 cm-long pendulum takes 2.50 minutes to undergo 104.1 complete oscillation cycles. (a) Compute the pendulum's period (in s). (b) Determine the acceleration due to gravity (in m/s²) at the place where the pendulum is located. m/s²A spring is attached to the ceiling and pulled 7 cm down from equilibrium and released. The amplitude decreases by 12% each second. The spring oscillates 17 times each second. Find an equation for the distance, D the end of the spring is below equilibrium in terms of seconds, t. D(t) =
- Mass and Spring: A 1.2 kg mass hangs in equilibrium from a spring. When the mass is displaced by 0.19 m and released from rest, it reaches a top speed of 1.2 m/s as it oscillates. A group of students records the motion of the spring for 321 seconds and deduces the system has a quality factor of Q = 1248. (a) What is the period of oscillation? (b) What is the spring constant of the spring?A simple pendulum has a length of 52.6 cm and makes 81.6 complete oscillations in 2.00 min. (a) Find the period of the pendulum. (b) Find the value of g at the location of the pendulum. m/s2A mass of 4.6 g is suspended from a massless spring of natural length 90 mm with the spring constant k = 3 Nm and causes the spring to extend by 10 mm. The mass is pulled down a further 5 mm and then released. Assuming g = 9.8 ms2, calculate the period of simple harmonic motion of the mass. Give your answer in Sl units.