Near the top of the citigroup center building in new york city, there is an object with mass of 4.00 ✕ 105 kg on springs that have adjustable force constants. its function is to dampen wind-driven oscillations of the building by oscillating at the same frequency as the building is being driven—the driving force is transferred to the object, which oscillates instead of the entire building.

(a) what effective force constant should the springs have to make the object oscillate with a period of 2.40 s?

(b) what energy is stored in the springs for a 2.20-m displacement from equilibrium?

Explanation:

It is given that,

Mass of an object,

(a) Time period of oscillation, T = 2.4 s

The formula for the time period of spring is given by :

Where

k is the force constant

(b) Displacement in the spring, x = 2.2 m

Energy stored in the spring is given by :

Hence, this is the required solution.

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation: