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For large t, every solution of d2 y dt2 + p dy dt + qy =

Differential Equations 00 | 4th Edition | ISBN: 9780495561989 | Authors: Paul (Paul Blanchard) Blanchard, Robert L. Devaney, Glen R. Hall ISBN: 9780495561989 199

Solution for problem 6 Chapter 4.4

Differential Equations 00 | 4th Edition

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Differential Equations 00 | 4th Edition | ISBN: 9780495561989 | Authors: Paul (Paul Blanchard) Blanchard, Robert L. Devaney, Glen R. Hall

Differential Equations 00 | 4th Edition

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Problem 6

For large t, every solution of d2 y dt2 + p dy dt + qy = cos t oscillates with angular frequency and amplitude A given by A(, p, q) = 1 (q 2)2 + p22 . That is, the amplitude A is a function of the parameters , p, and q. (a) Compute A/. (b) For fixed p and q, let M(p, q) denote the maximum value of A(, p, q) as a function of . Compute an expression for M(p, q). [Hint: This is a max-min problem from calculus.]

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Tuesday, 4/13/16 The “Second” New Deal Criticism on Roosevelt’s New Deal­­ the creation of the dependent class, so he pushes for... ● Social Security Act (August 14, 1935) ● WPA­­ Works Progress Administration ○ $11 billion works program (included the ex­slaves interviews) ○ Nation’s single largest employer ● Wagner Act, or National Labor Relations Act (July 5, 1935) ○ Guaranteed workers to organize without company interference ○ 3 million (1933) → 9 million (1939) Election of 1936 ● Most lopsided victory in American history (FDR won 61% of popular vote, 98% of the Electoral vote over Landon) ● Solidified the Democratic hold on power in the US ● But FDR’s second term wasn’t a good one: unemployment rate still stays at around 20% The End of Reform ● Judicial Reform ○ Aka the “Court­Packing Scheme” ○ FDR couldn’t get to the Supreme Court (they were getting in the way of the New Deal) *political cartoon (Constitution doesn’t say how many people in Congress there can be) ● World Affairs ○ FDR’s “Arsenal of Democracy” Fireside Chat, December 29, 1940 ■ Wanted to tell Americans to get involved World War II ● Started by Adolf Hitler­ wanted Germany to be the strongest power in Europe ○ Fascist­ wanted to use military force to get his goal ○ Knew Germany wasn’t strong enough ○ September 1, 1939­­ Germans invade Poland ○ In response Britain and France order them to surrender or them will start a war Appeasement (Hitler and Mussolini) 1. Economic Depression a. Interested in domestic problems, not national ones 2. Other foreign policy concerns 3. Sympathy for Germany a. Treaty of Versailles too harsh for the Germans b. Sympathy for Hitler and Mussolini 4. Dread of reliving the first World War a. 1 million British troops died in the war­ lots of deaths b. Most families had family member or friend killed or wounded in WWI British Prime Minister Neville Chamberlain “Peace in Our Time” (1938) We saved Britain and France once, we aren’t going to again, not interested What is our country doing (not only did we not do anything, but we took steps to ensure we wouldn’t get involved) ● The “merchants of death” view of WWI ● The Neutrality Acts ○ Sinking of the Lusitania­­ American’s cannot be on belligerent ships ○ FDR didn’t like this Defeat of France May 10, 1940­ Germany attacked France June, 1940­ France surrenders Americans were stunned that Germany defeated France­ France had advanced war material After the fall of France: 1. Burke­Wadsworth Act, Sept 1940 a. Peace­time act 2. Destroyers for bases, Sept 1940 3. Lend Lease, March 1941 (Notice it is AFTER FDR is re­elected in November 1940) a. US is at war with Germany Where does Japan fit in ● Military control of government ● Need for resources and living space ○ Attack on Manchuria, 1931 ○ Attack on China, 1937 ● Determination to take advantage of European War to make gains in Asia ● The attitude of the United States in an obstacle ○ Embargo, July 1941­ America cut off Japan’s access to metal and oil (we exported a lot, surprisingly) ○ Federalization of Philippine Army and Reinforcement of Philippine Garrison, July 1941 Japan is at war with China (China and America were friends) Japan attacked America! Pearl Harbor­ December 7, 1941 How did we get into war with Germany ­ When Hitler heard about Pearl Harbor he declared war with us ­ Congress may not have passed it if America decided to declare war with Germany America at War ***in textbook ● Some themes ○ The war of machines ■ Aircraft 1944 ● America: 96,000 ● Germany: 39,000 ● Japan: 28,000 ■ Major Ships: 1944 ● America: 2,247 ● Japan: 248 ■ Tanks 1943 ● America: 29,000 ● Germany: 17,000 ■ The US built these machines and built the machines to bring these machines over! (i.e. built the RRs, the ships) ■ The Depression helped the US­ because the unemployed were able to make war material so they had jobs ■ 4x as many people served in WWII than they did in WWI­ WWII veterans were the “greatest veterans” ○ The human cost of war ○ The “Good War” Draft Registration ● Married men were exempt from drafting ● Many people registered Casualties (Military only) ● America­ 16 million ○ 1 million dead and wounded ● Britain­ 6 million ○ 700,000 dead and wounded ● USSR­ Unknown ○ 20 million dead and wounded ● Germany­ 20 million ○ 10.4 million dead and wounded ● Note: as much as90%​ of all German casualties resulted from Germany’s war with the Soviet Union. ● New war­waging technologies­ allowed greater destruction than ever before ○ The Atom bombs ○ However, more Japanese civilians were killed by conventional bombs than the atom bomb ● Dehumanizing ideologies The Atomic Bomb ● Initial funding for research granted before the war began (1939­1940); Manhattan Project began in 1942 ● Fear was that GERMANY would get the bomb ● Mid­1945: Germany has surrendered. Japan clearly cannot win the war, but it HAS NOT been invaded and CANNOT be without great cost. ● What can compel Japan to surrender under terms (and at a cost) the allies will find acceptable Context for Decision Making about the use of the Atom Bomb: US casualties in the Pacific on the approach to Japan, 1944­1945 ● Philippines­ 48,000 ● Iwo Jima­ 30,000 ● Okinawa­ 51,000 Conditions of WWII caused very many people to die Dehumanizing of the enemy makes it easier to kill them WWII was seen as the “good” war, creating a more inclusive definition of citizenship Domestic Impact of the War: Catalyst for a more inclusive America ● America barely had any civilian casualties (as opposed to many dead in China, Britain, France, etc) Rationing ● Restrictions on excess use of material (fabric): no vests, trouser cuffs, double­breasted suits; pleated skirts, two­piece bathing suits became more common (used less cloth) ● Restrictions on private home construction ● Manufacturing of autos for private use was illegal (last one built Feb. 10, 1942) But not too much rationing ● “Farm times became good times.” ­­ farm wife in Idaho ● “Going to work in the navy yard, I felt like something had come down from heaven. The war completely turned my life around.” ­­ shipyard worker ● Macy’s Dept. Store chain had highest volume of one day sales in history (Dec 7, 1944) ● Even with rationing, civilian consumption rates rose markedly in the US from 1941­1945­­ the experience of ALL other countries at war was exactly the opposite of the United States’ experience Hardships, but no significant hardships African American and the War ● About 700,000 blacks moved out of the south ● Executive order 8802­­ banned discrimination in defense jobs ● About 1 million blacks served in the armed forces 75% of African Americans lived in the rural south going into WWII Some would go out west to work­­ a chance of new wealth, but racism did not stop Wendell Willkie (Republican candidate for president, 1940) ● “If we want to talk about freedom, we must mean freedom for everyone inside our frontiers.” One World, ​by Willkie ● Defeated by President Roosevelt Governor Frank Dixon, Alabama ● “The war emergency should not be used as a pretext to bring about the abolition of the color line.” ● I.e. things have to change once the war ends The Double “V” ­­ Victory over 1) the Nazis, and 2) racism Women war workers: some statistics ● By 1945, about ⅓ of working­age women are in the work force. About 2 million worked in defense industries (a 110% increase in the number of women working in industry) ● In peacetime, about ¼ of working­age women worked outside the home ● In war time, the majority of working­age women did not work outside the home ● 350,000 women served with the military World War II: A catalyst for internationalism (transforming the US from isolationist to one that embraced involvement in world affairs) ● Refused to join the “League of Nations” in 1919 ○ Established “United Nations” in 1945 ● Refused to forgive Europe’s war debts in the 1920s (under Coolidge) ○ Established the International Bank for reconstruction and development (the World Bank) ● Passed Isolationist Neutrality Acts in the 1930s ○ Joined Collective Security Organizations in the 1940s ● Passed protective tariffs in the 1920s and 1930s ○ General agreement on tariffs and trade (the WTO) in 1947 America wanting to be involved in foreign affairs led to PEACE AND PROSPERITY FOR ALL THE WORLD… OR THE COLD WAR The Cold War ● Soviet Union saw us taking over influence that they thought they should be taking ● Because the Germany was defeated, Soviet Union took over Europe, some of Korea, China, etc. and didn’t want to stop there ● Two great SUPERPOWERS: America and Soviet Union ● Stalin said capitalism and imperialism will make war certain to happen ● Winston Churchill and Harry Truman ○ Truman was the president ○ Did Churchill address Soviet Union ● Stalin was getting nervous that America was taking over ● America had Turkey and Stalin wanted it ○ Turkey was hostile to Russia ● Truman believed Stalin wanted to dominate the world ● Big powers were trying to make atomic weapons The US and USSR: Sources of tension ● General ○ Conflicting economic systems and ideologies ● Specific ○ Past history ■ WWI­­ communists took Russia out of the Allied camp in early 1918; US sent soldiers to North Russia and Siberia ■ Late recognition of Soviet regime ■ Russo­German non­aggression pact, 1939 (in 1939­1941, the USSR was an ally of Germany) ○ Status of Eastern Europe, and other Soviet actions in the 1940s ● Germany attacks Poland, Holland, Norway, Belgium, France, Britain­­ Soviet Union helps them (acts as an ally) ● Soviet Union betrayed/attacked Germany, and that’s when they were no longer allies Yalta Conference, Feb 1945 ● Big 3: US (Roosevelt), Britain (Churchill), and USSR­­ always met near the USSR border ● War isn’t over at this time, yet Germany is failing ● Meeting about post­war­ what will happen to Poland ● US (Roosevelt and Churchill) wanted Stalin to have self­determination­­ let the country pick their own government Potsdam Conference ● Roosevelt died and replaced by Truman ● Churchill replaced by Atley ● No agreement over Germany’s status ● Zones in Germany (American zone, British zone, French zone= WEST GERMANY), Soviet Zone= EAST GERMANY ● Stalin didn’t want an economically prosperous, powerful Germany, and America did William O. Douglas ● Stalin’s speech of February 1946 is “a declaration of WWIII” (Stalin’s speech says communism will ensure that war is avoided) ● Liberal Supreme Court Justice (from 1939­1975) James Forrestal “Venona” ● 1942­1945 Soviet Union launched an unrestrained espionage offensive against the US. It reached its peak when the US had a friendship with the USSR ● Late 1940s the evidence by Venona had American conclude that Stalin was going to betray the US… and they were right. George Kennan and the “Containment Doctrine” ● Soviet Union­­ extremist is the normal form of rule ● Foreigners were expected to be enemies ● USSR thinks that with the US, there can be no permanent m​odus vivendi. ​“way of living”) ● From the “Long Telegram” 1946, written by Mr. X (anonymously) ● How to push against the Soviet Union Containment The “Iron Curtain” speech ● Russians only admire military strength, so US needs to defeat them with our own strength Former Vice­President Henry Wallace ● We are still spending a lot on the military ● It would look to others that we didn’t want peace ● Roosevelt told the public that he wouldn’t keep Wallace as his vice­president We still never really knew what the Soviet wanted Josef Stalin ● “One death is a tragedy; one million deaths is a statistic.” ● Easy to see Stalin as Hitler You cannot appease dictators! ­­ Biggest lesson of WWII!

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Chapter 4.4, Problem 6 is Solved
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Textbook: Differential Equations 00
Edition: 4
Author: Paul (Paul Blanchard) Blanchard, Robert L. Devaney, Glen R. Hall
ISBN: 9780495561989

Since the solution to 6 from 4.4 chapter was answered, more than 265 students have viewed the full step-by-step answer. Differential Equations 00 was written by and is associated to the ISBN: 9780495561989. The answer to “For large t, every solution of d2 y dt2 + p dy dt + qy = cos t oscillates with angular frequency and amplitude A given by A(, p, q) = 1 (q 2)2 + p22 . That is, the amplitude A is a function of the parameters , p, and q. (a) Compute A/. (b) For fixed p and q, let M(p, q) denote the maximum value of A(, p, q) as a function of . Compute an expression for M(p, q). [Hint: This is a max-min problem from calculus.]” is broken down into a number of easy to follow steps, and 91 words. The full step-by-step solution to problem: 6 from chapter: 4.4 was answered by , our top Math solution expert on 01/02/18, 08:51PM. This textbook survival guide was created for the textbook: Differential Equations 00, edition: 4. This full solution covers the following key subjects: . This expansive textbook survival guide covers 90 chapters, and 1456 solutions.

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For large t, every solution of d2 y dt2 + p dy dt + qy =