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- How do you find the x displacement of particle 1?Consider a pendulum whose length is 22 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 = 2√ Determine the period in s. 4.4 x Your response differs from the correct answer by more than 10%. Double check your calculations. s 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 = Determine the natural frequency in Hz. 0.227 Your response differs from the correct answer by more than 10%. Double check your calculations. HzIf you did the previous question right, you hopefully got an expression for yo. You may notice that you can simplify the differential equation a little bit: d'y k (y – yo) dt2 т The parameter yo now plays the roll of the "relaxed length". A better term may be "equilibrium value for y". But mathematically, it's identical to a relaxed length with the spring as the only force. We continue using this equation: y(t) = Y0 + A cos(wt + y) Now, solve for A (in cm) with these parameters. Again, if you need more information, enter -100000. The parameters are: •m = 200 grams • Yo = (equilibrium value) = 40 cm • k = (spring constant) = 0.03 N/cm
- Suppose a large spherical object, such as a planet, with radius R and mass M has a narrow tunnel passing diametrically through it. A particle of mass m is inside the tunnel at a distance x ï. Part A Find an expression for the magnitude of the gravitational force on the particle, assuming the object has uniform density. Express your answer in terms of the variables x, R, m, M, and gravitational constant G.Write down the expression for period of a pendulum of length I and the gravitational field strength g. Please use square root and power please use sqrt(A*B) and (A*B)^2. Please use the "Display response" button to check you entered the answer you expect. "*" for products (e.g. B*A), "/" for ratios (e.g. B/A) and the usual "+" and "-" signs as appropriate. For T= Display responsePart A) Find the period of the second hand of a wall clock. Express your answer in seconds to three significant figures. Part B) Find the frequency of the second hand of a wall clock. Express your answer in hertz to three significant figures. Part C) Find the angular frequency of the second hand of a wall clock. Express your answer in radians per second to three significant figures. Part D) Find the period of the minute hand of a wall clock. Express your answer in seconds to three significant figures. Part E) Find the frequency of the minute hand of a wall clock. Express your answer in hertz to three significant figures. Part F) Find the angular frequency of the minute hand of a wall clock. Express your answer in radians per second to three significant figures.
- Anilquestion d and e please For any vector quantity, be sure to always include the magnitude and direction(teacher asked)1. A 97 g ball bobbing up and down on the ocean as the waves roll by has a vertical position that can be described as a function of time by x(t) = cos(10t). What is the force on the ball at a time of 4.6 seconds? Note: The argument of the cosine function is in radians. Hint: Don't forget the sign of the force. F = 6.74 X√ N
- For the machine element shown, locate the y coordinate of the center of gravity.The analysis of a simple pendulum assumed that the mass was a particle, with no size. A realistic pendulum is a small, uniform sphere of mass M and radius R at the end of a massless string, with I being the distance from the pivot to the center of the sphere. Part A Find an expression for the period of this pendulum. Express your answer in terms of the variables M, R, L, and free fall acceleration g. T= IVE ΑΣΦ Submit Part B Request Answer Suppose M = 25 g, R = 1.0 cm, and L = 1.0 m, typical values for a real pendulum. What is the ratio Treal/Tsimple, where Treal is your expression from part A and T'simple = 2π₁/₂ Express your answer using six significant figures. Treal/Tsimple= ? IVE ΑΣΦ ?Part A: The position of a 40 gg oscillating mass is given by x(t)=(2.0cm)cos(10t)=(2.0cm)cos(10t), where t is in seconds. Determine the velocity at t=0.40s=0.40s. Express your answer in meters per second to two significant figures. Part B: Assume that the oscillating mass described in Part A is attached to a spring. What would the spring constant k of this spring be? Express your answer in newtons per meter to two significant figures. Part C: What is the total energy E of the mass described in the previous parts? Express your answer in joules to two significant figures.