You run to the foot of the portcullis. In front of it you find two one-kilogram

Question

You run to the foot of the portcullis. In front of it you find two one-kilogram masses, five 1 gram masses, a one meter length of rope, and a selection of springs labeled 1 N/m, 10 N/m, and 100 N/m. A complicated looking locking mechanism has two hooks protruding from it. A small copper plaque says “Match the frequencies and raise the gate!” It also bears a diagram of a mass on a spring and a pendulum swinging side by side. From the available selection of masses and springs and the section of rope, can you build a pendulum and a mass on a spring such that you can find an angular frequency that matches and open the gate?

Explanation / Answer

Their problem is a very complicated and difficult to understand statement, but I think you need to build two oscillatory systems is a spring-mass and pendulum have equal angular velocity

Expression for the angular velocity

spring-mass

w2= K/m

pendulum

w22= g/L

to have equal sides

w1 =w2

K/m = g/l

Data

m = 1 kg quantity 2

m = 0.001 g quantity 5

K =1, 10, 100

L= 1 m

calculate

w22= g/L

w22= 9.8 / 1

w22= 9.8 rad/s2

We use this w2

w12 = 9.8 = K/m

K/m = 9.8 = 10

Calculations were performed with w2 spring-mass for ease of making combinations

combinations

* K = 10 N/m m = 1 Kg

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