Show that your resting pulse occurs at a time interval that corresponds to the period of...
The period T of a simple pendulum is given by T=2πLg−−√T=2πLg where L is the length of the pendulum and g is the acceleration due to gravity. Assume that g = 9.80 m/s2 exactly, and that L, in meters, is lognormal with parameters μL = 0.8 and σ2L=0.05.σL2=0.05. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Find P(T > 3).
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...
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...
(radians) from the vertical. It can be shown that as a function of time satisfies the (1 point) Suppose a pendulum with length L (meters) has angle differential equation: d20 + & sin 0 = 0 dt 2 L where g = 9.8 m/sec/sec is the acceleration due to gravity. For small values of we can use the approximation sin() ~ 0, and with that substitution, the differential equation becomes linear. A. Determine the equation of motion of a pendulum...
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Borough of Manhatan Community College The City University of New York SCIENCE DEPARTMENT Laboratory Experiment ACCELERATION DUE TO GRAVITY USING A SIMPLE PENDULUM To calculate the value of the acceleration due to gravity by measuring the period of a pendulum with four different lengths. Apparatus Drilled steel ball, string, clamp, support to hold pendulum apparatus, meter stick, and timer Theory:...
PROBLEMS. Answer the following questions by justifying your answer. Show work where applicable. The period, T, of a pendulum is the time it takes for a pendulum to swing back and forth once. If the dimensional quantities that a period have depend on gravity, g, and the length of the pendulum, write an equation for T expressed in terms of the fundamental properties of g and L. Given h/mv = λ , determine the wavelength of an electron with a...
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(1 point) Suppose a pendulum with length L (meters) has angle 0 (radians) from the vertical. It can be shown that 0 as a function of time satisfies the differential equation: d20 +sin0 0 dt2 where g 9.8 m/sec/sec is the acceleration due to gravity. For small values of 0 we can use the approximation sin(0)~0, and with that substitution, the differential equation becomes linear. A. Determine the equation of motion of a pendulum with length...
Pre-Lab Q2: Consider the equation you will use to calculate the period of your pendulum. For each scenario below, determine how an error in your length measurement (L) would affect your predicted period value (T) SCENARIO 1: You measured the pendulum length (L) to be LARGER than the actual value. As a result your predicted period (T) will be a. i. ii. LARGER than the actual value. SMALLER than the actual value. b. SCENARIO 2: You measured the pendulum length...
e correct answerís) unambiguously. Show your work for partial credit. 1. The period of a pendulum is the time it takes the pendulum to swing back and forth once. If ties that the period depends on are the acceleration of gravity,g and the length of the pendulum, I, what combination of g and I must the period be proportional to? (Acceleration has SI units of m/s) (a) g/l (b) gl (d) gl2 2. An apple falls from an apple tree...
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4. Extra Creait: 10 pts The period of a pendulum with length L that makes a maximum angle of 690 with the vertical is dx T/2 1-k2 sin (x) where k =sin (160) and g is the acceleration due to gravity. Expand the integrand as a binomial series to show that 12123212352 224262 2242 1.3.5-....(n-1) . π when n is even Hint: You'll need to use the fact that for/2sin"(x)dx = Note that this...