A simple pendulum with a length of 2.23 m and a mass of 6.74 kg is given an initial speed of 2.06 m/s at its equilibrium position. Assume it undergoes simple harmonic motion. Determine (a) its period, (b) its total energy, and (c) its maximum angular displacement.

A 15-centimeter pendulum moves according to the equation θ = 0.2 cos 8t, where θ is the angular displacement from the vertical in radians and t is the time in seconds. Determine the maximum angular displacement and the rate of change of θ when t=3 seconds.

A load of 50 N attached to a spring hanging vertically stretches the spring 5.0 cm. The spring is now placed horizontally on a table and stretched 11 cm. What force is required to stretch the spring by that amount?

For each of the following pdfs let X1, …, Xn be iid observations. Find a complete sufficient statistic, or show that one does not exist. (a) $f(x | \theta)=\frac{2 x}{\theta^{2}}$, 0 < x < $\theta$, $\theta$ > 0 (b) $f(x | \theta)=\frac{\theta}{(1+x)^{1+\theta}}$ , 0 < x < $\infty$, $\theta$ > 0 (c) $f(x | \theta)=\frac{(\log \theta) \theta^{x}}{\theta-1}$, 0 < x < 1, $\theta$ > 1, (d)

$$f(x | \theta)=\left(\begin{array}{l}{2} \\ {x}\end{array}\right) \theta^{x}(1-\theta)^{2-x}$$

, f(x|$\theta$) = e−(x − $\theta$) exp(−e−(x − $\theta$)), $-\infty<x<\infty,-\infty<\theta<\infty$(e) , x = 0, 1, 2, $0 \leq \theta \leq 1$

An object is undergoing SHM with period 0.300 s and amplitude 6.00 cm. At t = 0 the object is instantaneously at rest at x = 6.00 cm. Calculate the time it takes the object to go from x = 6.00 cm to x = -1.50 cm

Review. As an astronaut, you observe a small planet to be spherical. After landing on the planet, you set off, walking always straight ahead, and find yourself returning to your spacecraft from the opposite side after completing a lap of 25.0 km. You hold a hammer and a falcon feather at a height of 1.40 m, release them, and observe that they fall together to the surface in 29.2 s. Determine the mass of the planet.

Water (p=1000 kg/m3) is accelerated from rest in a horizontal pipe that is 80 m long and 30 cm in diameter. If the acceleration rate (toward the downstream end) is 5 m/s2, what is the pressure at the upstream end if the pressure at the downstream end is 90 kPa gage?

An object in SHM oscillates with a period of 4.0 s and an amplitude 10 cm. How long does the object take to move from x = 0.0 cm to x = 6.0 cm?

A 0.500-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.0 cm. Calculate the maximum value of its speed when the object is 6.00 cm from the equilibrium position.

In a given city it is assumed that the number of automobile accidents in a given year follows a Poisson distribution. In past years the average number of accidents per year was 15, and this year it was 10. Is it justified to claim that the accident rate has dropped?

Review. Photons of wavelength λ are incident on a metal. The most energetic electrons ejected from the metal are bent into a circular arc of radius R by a magnetic field having a magnitude B. What is the work function of the metal?

A $0.40-\mathrm{kg}$ object is attached to a spring with force constant $160 \mathrm{~N} / \mathrm{m}$ so that the object is allowed to move on a horizontal frictionless surface. The object is released from rest when the spring is compressed $0.15 \mathrm{~m}$. Find (b) its acceleration at that instant.

A $0.40-\mathrm{kg}$ object is attached to a spring with force constant $160 \mathrm{~N} / \mathrm{m}$ so that the object is allowed to move on a horizontal frictionless surface. The object is released from rest when the spring is compressed $0.15 \mathrm{~m}$. Find (a) the force on the object and

The frequency of vibration of an object-spring system is $5.00 \mathrm{~Hz}$ when a $4.00-\mathrm{g}$ mass is attached to the spring. What is the force constant of the spring?