Question

10 You have carried out an experiment to investigate the effect of the length of a pendulum on the time period of oscillation. Theory says that the pendulum should follow the rule T = 2? ?(L/g) Where T is the time period (seconds) L is the length of the pendulum (metre) G is the acceleration due to gravity (g=9.81m/s²) Calculate the expected percentage error in the time period calculation if your measurement of length is 1% high. A3 Power series Definitions: a power series as f(x) = a0 + a1x + a2x² + a3x³ + ... + anx? a Taylor series as f(x) = f(a) + f'(a)(x-a) + f''(a)/2!(x-a)² + ... + f?(a)/n!(x-a)? Routine operations involve: a Maclaurin series as a Taylor series with a = 0 convergence and divergence conditions for convergence and divergence. Non-routine operations involve: numerical value for e using a power series proof that d/dx(e?) = e? using series engineering applications, e.g. error in area or volume for small error in measurement of length, oscillator frequency for an electrical circuit if components have small errors in their values.

          10 You have carried out an experiment to investigate the effect of the length of a pendulum on the time period of oscillation. Theory says that the pendulum should follow the rule
T = 2? ?(L/g)
Where T is the time period (seconds)
L is the length of the pendulum (metre)
G is the acceleration due to gravity (g=9.81m/s²)
Calculate the expected percentage error in the time period calculation if your measurement of length is 1% high.
A3 Power series
Definitions:
a power series as f(x) = a0 + a1x + a2x² + a3x³ + ... + anx?
a Taylor series as f(x) = f(a) + f'(a)(x-a) + f''(a)/2!(x-a)² + ... + f?(a)/n!(x-a)?
Routine operations involve:
a Maclaurin series as a Taylor series with a = 0
convergence and divergence
conditions for convergence and divergence.
Non-routine operations involve:
numerical value for e using a power series
proof that d/dx(e?) = e? using series
engineering applications, e.g. error in area or volume for small error in measurement of length, oscillator frequency for an electrical circuit if components have small errors in their values.

10 You have carried out an experiment to investigate the effect of the length of a pendulum on the time period of oscillation. Theory says that the pendulum should follow the rule
T = 2? ?(L/g)
Where T is the time period (seconds)
L is the length of the pendulum (metre)
G is the acceleration due to gravity (g=9.81m/s²)
Calculate the expected percentage error in the time period calculation if your measurement of length is 1% high.
A3 Power series
Definitions:
a power series as f(x) = a0 + a1x + a2x² + a3x³ + ... + anx?
a Taylor series as f(x) = f(a) + f'(a)(x-a) + f”(a)/2!(x-a)² + ... + f?(a)/n!(x-a)?
Routine operations involve:
a Maclaurin series as a Taylor series with a = 0
convergence and divergence
conditions for convergence and divergence.
Non-routine operations involve:
numerical value for e using a power series
proof that d/dx(e?) = e? using series
engineering applications, e.g. error in area or volume for small error in measurement of length, oscillator frequency for an electrical circuit if components have small errors in their values.

Added by Anna G.

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