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1: Use dimensional analysis to derive the expression for the time period of oscillations of a...
A simple pendulum consists of a ball of mass M hanging from a uniform string of...
A simple pendulum consists of a ball of mass M hanging from a uniform string of mass m and length L, with m << M. (a) If the period of oscillations for the pendulum is T, derive an expression for the speed of a transverse wave in the string when the pendulum hangs at rest in terms of m, M, T and g (the acceleration due to gravity). Your expression should not include L. (b) If the string is made...
The period T of a simple pendulum with small oscillations is calculated from the formula T=2pi sqrt(L/g) where L is the...
The period T of a simple pendulum with small oscillations is calculated from the formula T=2pi sqrt(L/g) where L is the length of the pendulum and g is the acceleration due to gravity. suppose that measured values of L and g have errors and are corrected with new values where L is increased from 4m to 4.5m and g is increased from 9 m/s2 to 9.8 m/s2. Use differentials to estimate the change in the period. Does the period increase...
The period of a pendulum (i.e. the time it takes to swing back and forth over...
The period of a pendulum (i.e. the time it takes to swing back and forth over one cycle of motion) can credibly be believed to depend on both the length of the pendulum and the acceleration due to gravity. We can write this as Where C is some unknown constant, L is the length of the pendulum, g is the acceleratio lue to gravity, and x and y are unknown. Using dimensional analysis, determine how T lepends on L and...
Dimensional Analysis: Often, we can almost derive formulas (up to an overall constant) just by knowing...
Dimensional Analysis: Often, we can almost derive formulas (up to an overall constant) just by knowing the units of the relevant quantities. Under the assumption that the pendulum's period can only depend on the pendulum's length L, m, maximum angle 0, and the strength of gravity g (with units [g]=m/s2), explain why we must have a relation like mass L T f(0) (Note that 0 counts as a unitless parameter here.) Asserting f(0)~ f(0) in this formula is the small...
An expression for the period of a simple pendulum with string length ℓ derived using calculus...
An expression for the period of a simple pendulum with string
length ℓ derived using calculus is T = 2(pi)sqrt{ ℓ /g } . Where g
is the acceleration due to gravity. Use the data in the table to
decide whether or not the pendulum in the experiment can be
considered a simple pendulum. Explain your decision.
Suppose have the ability to vary the mass m of the bob and the length f of the string. You decide to to...
Consider a simple pendulum consisting of a massive bob suspended from a fixed point by a...
Consider a simple pendulum consisting of a massive bob suspended from a fixed point by a string. Let T denote the time (period of the pendulum) that it takes the bob to complete one cycle of oscillation. How does the period of the simple pendulum depend on the quantities that define the pendulum and the quantities that determine the motion? [You need to perform a dimensional analysis to solve this one. Start by assuming T = k Inmpgq, where k...
The period T of a simple pendulum is the amount of time required for it to...
The period T of a simple pendulum is the amount of time required for it to undergo one complete oscillation. If the length of the pendulum is L and the acceleration of gravity is g, then T is given by: T=2πL^pG^q Find the powers p and q required for dimensional consistency. Enter your answers numerically separated by a comma.
Please do all questions and show work. 1. (2 points) A 200 g mass attached to...
Please do all questions and show work.
1. (2 points) A 200 g mass attached to a light spring oscillates on a frictionless, horizontal table. The mass is pulled 8 cm and released. A student finds that 12 oscillations takes 18 seconds. (a) What is the spring constant? (b) What is the maximum speed of the mass? 2. (3 points) The position of an object connected to a spring varies with time according to the expression x = (7.5 cm)cos...
Length L (m) Time period T(sec) 0.8 0.3 0.45 0.61 0.75 0.91 1.03 1.2 1.35 1.3...
Length L (m) Time period T(sec) 0.8 0.3 0.45 0.61 0.75 0.91 1.03 1.2 1.35 1.3 1.7 1.9 2.0 2.2 2.3 The time period (time for one oscillation) of a simple pendulum depends on the length of pendulum. This above data set includes time periods T for different length of pendulum. Show the final form of functional dependence of time period T on L. For functional dependence, repeat the analysis using pre-made graph to find value of n.
B. Rotational System (0-4) Find the theoretically predicted period of the torsional pendulum. Derive an expression...
B. Rotational System (0-4) Find the theoretically predicted period of the torsional pendulum. Derive an expression for Tos in terms of the torsional spring constant (r) and the rotational inertia of the disk (1) Find the torsional spring constant. 15.0cm 7.50 cm radius Torsion lathe diameter hanging mass (g) 50 torque (Nm) 150 250 350 450 37.5 46-2 55-3 G3.1 71.1 angular position (deg) angular position (rad) We were unable to transcribe this imageA. Translational System (Q-1) Find the theoretically...
The period of a pendulum (i.e. the time it takes to swing back and forth over one cycle of motion) can credibly be believed to depend on both the length of the pendulum and the acceleration due to gravity. We can write this as Where C is some unknown constant, L is the length of the pendulum, g is the acceleratio lue to gravity, and x and y are unknown. Using dimensional analysis, determine how T lepends on L and...
Dimensional Analysis: Often, we can almost derive formulas (up to an overall constant) just by knowing the units of the relevant quantities. Under the assumption that the pendulum's period can only depend on the pendulum's length L, m, maximum angle 0, and the strength of gravity g (with units [g]=m/s2), explain why we must have a relation like mass L T f(0) (Note that 0 counts as a unitless parameter here.) Asserting f(0)~ f(0) in this formula is the small...
An expression for the period of a simple pendulum with string
length ℓ derived using calculus is T = 2(pi)sqrt{ ℓ /g } . Where g
is the acceleration due to gravity. Use the data in the table to
decide whether or not the pendulum in the experiment can be
considered a simple pendulum. Explain your decision.
Suppose have the ability to vary the mass m of the bob and the length f of the string. You decide to to...
Consider a simple pendulum consisting of a massive bob suspended from a fixed point by a string. Let T denote the time (period of the pendulum) that it takes the bob to complete one cycle of oscillation. How does the period of the simple pendulum depend on the quantities that define the pendulum and the quantities that determine the motion? [You need to perform a dimensional analysis to solve this one. Start by assuming T = k Inmpgq, where k...
Please do all questions and show work.
1. (2 points) A 200 g mass attached to a light spring oscillates on a frictionless, horizontal table. The mass is pulled 8 cm and released. A student finds that 12 oscillations takes 18 seconds. (a) What is the spring constant? (b) What is the maximum speed of the mass? 2. (3 points) The position of an object connected to a spring varies with time according to the expression x = (7.5 cm)cos...
Length L (m) Time period T(sec) 0.8 0.3 0.45 0.61 0.75 0.91 1.03 1.2 1.35 1.3 1.7 1.9 2.0 2.2 2.3 The time period (time for one oscillation) of a simple pendulum depends on the length of pendulum. This above data set includes time periods T for different length of pendulum. Show the final form of functional dependence of time period T on L. For functional dependence, repeat the analysis using pre-made graph to find value of n.
B. Rotational System (0-4) Find the theoretically predicted period of the torsional pendulum. Derive an expression for Tos in terms of the torsional spring constant (r) and the rotational inertia of the disk (1) Find the torsional spring constant. 15.0cm 7.50 cm radius Torsion lathe diameter hanging mass (g) 50 torque (Nm) 150 250 350 450 37.5 46-2 55-3 G3.1 71.1 angular position (deg) angular position (rad) We were unable to transcribe this imageA. Translational System (Q-1) Find the theoretically...
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