Homework Help is Here – Start Your Trial Now!
Science
Advanced Physics
Somewhere on a distant planet -- substantially larger than Earth -- gravity works just like does here, but provides a different and (as yet) unknown constant value for free-fall acceleration There, a particle of mass m is dangled from a long string, length L; the particle oscillates along a small arc according to the differential equation d²0 dt² Here, refers to an angular displacement measured from the vertical and t refers to time. = -250. The particle's mass is given by m = 3 kg. The length of the string is given by L = 2 meters. Whenever the particle arrives at a location of 0 = (1/10) radians from the vertical, the particle has no instantaneous speed. On both sides of the vertical, that is, = (1/10) radians is repeatedly observed to be a 'turning point' for the particle's periodic motion. i. Draw a clear FREE-BODY diagram of this particle at some arbitrary point during oscillation, making sure to label variables and constants described above. ii. Approximating the number of Hertz to three significant digits if necessary, what is the standard frequency of this oscillator on a string? iii. Approximating to three significant digits if necessary, how many seconds should we expect this pendulum to take in order to get from one turning point to its equilibrium position (to a fully vertical orientation)?

Somewhere on a distant planet -- substantially larger than Earth -- gravity works just like does here, but provides a different and (as yet) unknown constant value for free-fall acceleration There, a particle of mass m is dangled from a long string, length L; the particle oscillates along a small arc according to the differential equation d²0 dt² Here, refers to an angular displacement measured from the vertical and t refers to time. = -250. The particle's mass is given by m = 3 kg. The length of the string is given by L = 2 meters. Whenever the particle arrives at a location of 0 = (1/10) radians from the vertical, the particle has no instantaneous speed. On both sides of the vertical, that is, = (1/10) radians is repeatedly observed to be a 'turning point' for the particle's periodic motion. i. Draw a clear FREE-BODY diagram of this particle at some arbitrary point during oscillation, making sure to label variables and constants described above. ii. Approximating the number of Hertz to three significant digits if necessary, what is the standard frequency of this oscillator on a string? iii. Approximating to three significant digits if necessary, how many seconds should we expect this pendulum to take in order to get from one turning point to its equilibrium position (to a fully vertical orientation)?

icon
Related questions
Question

I need detailed answers. Thanks

III Ticque-Tocque Somewhere on a distant planet -- substantially larger than Earth -- gravity works just like it does here, but provides a different and (as yet) unknown constant value for free-fall acceleration. There, a particle of mass m is dangled from a long string, length L; the particle oscillates along a small arc according to the differential equation d²0 dt² = -250. Here, refers to an angular displacement measured from the vertical and t refers to time. The particle's mass is given by m = 3 kg. The length of the string is given by L = 2 meters. Whenever the particle arrives at a location of 0 = 1/10) radians from the vertical, the particle has no instantaneous speed. On both sides of the vertical, that is, = (1/10) radians is repeatedly observed to be a 'turning point' for the particle's periodic motion. i. Draw a clear FREE-BODY diagram of this particle at some arbitrary point during oscillation, making sure to label variables and constants described above. ii. Approximating the number of Hertz to three significant digits if necessary, what is the standard frequency of this oscillator on a string? iii. Approximating to three significant digits if necessary, how many seconds should we expect this pendulum to take in order to get from one turning point to its equilibrium position (to a fully vertical orientation)? iv. What is the particle's approximate SPEED at t = T/4 seconds? (for which I stands for 'Period' of this pendulum). v. Break up your pure FBD into components. Given your component diagram, Show how the angular frequency for a pendulum is determined fully by parameters: That is, show that harmonic oscillation will occur at a rate which depends on the length of the string and on the free-fall acceleration constant due to gravity. vi. According to your finding in v (above), determine the value for g at the location this pendulum swings. Go back to part iv, above: Show how you can use this finding for g to compute a numerical value for speed at t = T/4. SHOW how two distinct solution methods can serve to check one final numerical answer for instantaneous speed at t = T/4.
Transcribed Image Text:III Ticque-Tocque Somewhere on a distant planet -- substantially larger than Earth -- gravity works just like it does here, but provides a different and (as yet) unknown constant value for free-fall acceleration. There, a particle of mass m is dangled from a long string, length L; the particle oscillates along a small arc according to the differential equation d²0 dt² = -250. Here, refers to an angular displacement measured from the vertical and t refers to time. The particle's mass is given by m = 3 kg. The length of the string is given by L = 2 meters. Whenever the particle arrives at a location of 0 = 1/10) radians from the vertical, the particle has no instantaneous speed. On both sides of the vertical, that is, = (1/10) radians is repeatedly observed to be a 'turning point' for the particle's periodic motion. i. Draw a clear FREE-BODY diagram of this particle at some arbitrary point during oscillation, making sure to label variables and constants described above. ii. Approximating the number of Hertz to three significant digits if necessary, what is the standard frequency of this oscillator on a string? iii. Approximating to three significant digits if necessary, how many seconds should we expect this pendulum to take in order to get from one turning point to its equilibrium position (to a fully vertical orientation)? iv. What is the particle's approximate SPEED at t = T/4 seconds? (for which I stands for 'Period' of this pendulum). v. Break up your pure FBD into components. Given your component diagram, Show how the angular frequency for a pendulum is determined fully by parameters: That is, show that harmonic oscillation will occur at a rate which depends on the length of the string and on the free-fall acceleration constant due to gravity. vi. According to your finding in v (above), determine the value for g at the location this pendulum swings. Go back to part iv, above: Show how you can use this finding for g to compute a numerical value for speed at t = T/4. SHOW how two distinct solution methods can serve to check one final numerical answer for instantaneous speed at t = T/4.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 15 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question

I need a detailed explanation for these. Thank you

iv. What is the particle's approximate SPEED at t = T/4 seconds? (for which I stands for 'Period' of this pendulum). v. Break up your pure FBD into components. Given your component diagram, Show how the angular frequency for a pendulum is determined fully by parameters: That is, show that harmonic oscillation will occur at a rate which depends on the length of the string and on the free-fall acceleration constant due to gravity. vi. According to your finding in v (above), determine the value for g at the location this pendulum swings. Go back to part iv, above: Show how you can use this finding for g to compute a numerical value for speed at t = T/4. SHOW how two distinct solution methods can serve to check one final numerical answer for instantaneous speed at t = T/4.
Transcribed Image Text:iv. What is the particle's approximate SPEED at t = T/4 seconds? (for which I stands for 'Period' of this pendulum). v. Break up your pure FBD into components. Given your component diagram, Show how the angular frequency for a pendulum is determined fully by parameters: That is, show that harmonic oscillation will occur at a rate which depends on the length of the string and on the free-fall acceleration constant due to gravity. vi. According to your finding in v (above), determine the value for g at the location this pendulum swings. Go back to part iv, above: Show how you can use this finding for g to compute a numerical value for speed at t = T/4. SHOW how two distinct solution methods can serve to check one final numerical answer for instantaneous speed at t = T/4.
Somewhere on a distant planet -- substantially larger than Earth -- gravity works just like it does here, but provides a different and (as yet) unknown constant value for free-fall acceleration. There, a particle of mass m is dangled from a long string, length L; the particle oscillates along a small arc according to the differential equation d²0 dt² = -250. Here, e refers to an angular displacement measured from the vertical and t refers to time. The particle's mass is given by m = 3 kg. The length of the string is given by L = 2 meters. Whenever the particle arrives at a location of 0=1/10) radians from the vertical, the particle has no instantaneous speed. On both sides of the vertical, that is, = (1/10) radians is repeatedly observed to be a 'turning point' for the particle's periodic motion.
Transcribed Image Text:Somewhere on a distant planet -- substantially larger than Earth -- gravity works just like it does here, but provides a different and (as yet) unknown constant value for free-fall acceleration. There, a particle of mass m is dangled from a long string, length L; the particle oscillates along a small arc according to the differential equation d²0 dt² = -250. Here, e refers to an angular displacement measured from the vertical and t refers to time. The particle's mass is given by m = 3 kg. The length of the string is given by L = 2 meters. Whenever the particle arrives at a location of 0=1/10) radians from the vertical, the particle has no instantaneous speed. On both sides of the vertical, that is, = (1/10) radians is repeatedly observed to be a 'turning point' for the particle's periodic motion.
Solution
Bartleby Expert
SEE SOLUTION