Please provide solutions so I can understand them better. Thank you

1. A simple pendulum of length L has a period of T seconds. What should be the length for the period to be 37 seconds? 2. The equation of a vibrating object is . = 27.2 cos 27(8.56); meters. (a) What is the amplitude of vibration? (b) What is the frequency? (c) What is the period? 3 . The maximum possible efficiency of a reversible heat engine is 79.46% when the cold temperature is 224.0 C. What is the hot temperature in degrees Celsius? 4. A 1.4-cm tall object is 3.2 cm in front of a converging lens with a focal length of 1.8 cm. Use the mirror-thin lens equation to find the image distance and image height. . Point charge A is composed of 3.46 x 1010 electrons. It is 0.536 millimeters from point charge B. which is composed of 4.32 x 10 2 electrons. (a) What is the total charge at each point? (b) What is the magnitude of the force that the charges exert on each other? Two positive point charges of 7.2 x 10- C and 4.3 x 10-8 C. respectively, exert a 1 1.2-N force on each other. What distance separates the two charges? 7. A 24-volt battery and a 1525-$ resistor are used to charge four 1525 0 capacitors, as shown. The capacitors C1. C2, C3. and C4 have values of $5.0 UF. 44.0 UF. 19.0 HF. and 88.0 UF, respectively. 24 V C , C2 C3 C4 (a) What is the equivalent capacitance? (b) The switch is closed. What is the charging time constant? 8. A banjo string 0.35 meter long has a fundamental frequency of 725 Hz. What is the speed of a wave on this string? 9. A reversible adiabatic process is used to drive a flywheel. A piston whose area is 0.465 m- compresses air a distance of 0.155 m with a pressure of 17.300 pascals. What is the change in internal energy of the air in the cylinder? 10. The negative charge at A causes an electric field on P as shown and has a magnitude of 1.9 x 10' newtons per coulomb. The 1.9 x 107 N charge at B is negative 3.4 x 1070 coulomb. Find the electric field at P caused by the two charges. 5.0 cm 4.0 cm A- - B 3.0 cm